Analysis of iconic words and gestures

1 Introduction

This analysis is going to look at the count of gestures as a function whether the concomitant word is iconic or not.

There are three main variables:

• gesture yes/no, which includes all types gestures (iconic, deictic, beat, metaphoric)
• iconic_gesture yes/no, which looks at whether those videos with a gesture also feature an iconic gesture
• a third variable, non_iconic_gesture, which is gesture - iconic gesture is constructed in the script

The models will not be computed in the markdown due to the long estimation time. This is why the code chunks will have eval = FALSE as setting. Instead, the pre-compiled models are loaded into R from the models folder.

2 Setup

Let’s load packages:

# Load packages:

library(tidyverse) # for data processing and visualization
library(patchwork) # for multi-plot arrays
library(brms) # for bayesian analysis
library(effsize) # for Cohen's d effect size

For reproducibility, report version numbers:

R.Version()$version.string

## [1] "R version 4.4.0 (2024-04-24)"

packageVersion('tidyverse')

## [1] '2.0.0'

packageVersion('patchwork')

## [1] '1.2.0'

packageVersion('brms')

## [1] '2.21.0'

Load data:

df <- read_csv('../data/ALL_videos_coded_18_06_24.csv')

Let’s get rid of everything that doesn’t have a number, which are the ones that have not been coded.

df <- filter(df, !is.na(word_used))

Let’s make the word column lowercase:

df <- mutate(df, word = str_to_lower(word))

3 Overview and exclusions

Let’s see for how many the word wasn’t there?

df |> 
  count(word_used) |> 
  mutate(proportion = n / sum(n))

## # A tibble: 2 × 3
##   word_used     n proportion
##       <dbl> <int>      <dbl>
## 1         0  1921      0.336
## 2         1  3804      0.664

Let’s reduce the data frame to only those cases where word_used is equal to 1.

df <- filter(df, word_used == 1)

Let’s do a count of the duplicates:

df |> 
  count(not_duplicate) |> 
  mutate(proportion = n / sum(n))

## # A tibble: 2 × 3
##   not_duplicate     n proportion
##           <dbl> <int>      <dbl>
## 1             0   682      0.179
## 2             1  3122      0.821

Let’s get rid of the duplicates:

df <- filter(df, not_duplicate == 1)

Let’s count whether the speaker was visible:

df |> 
  count(speaker_visible) |> 
  mutate(proportion = n / sum(n))

## # A tibble: 2 × 3
##   speaker_visible     n proportion
##             <dbl> <int>      <dbl>
## 1               0   899      0.288
## 2               1  2223      0.712

Let’s take only those for which the speaker is visible:

df <- filter(df, speaker_visible == 1)

Let’s count whether the hands were visible:

df |> 
  count(hands_visible) |> 
  mutate(proportion = n / sum(n))

## # A tibble: 2 × 3
##   hands_visible     n proportion
##           <dbl> <int>      <dbl>
## 1             0   601      0.270
## 2             1  1622      0.730

Let’s take only those for which the hands are visible:

df <- filter(df, hands_visible == 1)

Let’s count whether the hands were free:

df |> 
  count(hands_free) |> 
  mutate(proportion = n / sum(n))

## # A tibble: 2 × 3
##   hands_free     n proportion
##        <dbl> <int>      <dbl>
## 1          0    76     0.0469
## 2          1  1546     0.953

The 0’s here include only those cases for which it was clearly impossible for the speaker to gesture. So, we’ll gesture.

df <- filter(df, hands_free == 1)

Not 100% sure about this, but for now, let’s make the iconic_gesture cases that have 0 for the gesture column into NA, just so we don’t treat those as non-iconic gestures by accident.

df <- mutate(df,
             iconic_gesture = ifelse(gesture == 0, 0, iconic_gesture))

For plotting later, it makes sense to switch the non_iconic label to a less techy-looking non-iconic, and also change the order so that the non-iconic level then comes first:

df <- mutate(df,
             type = ifelse(type == 'non_iconic',
                           'non-iconic \nword', 'iconic \nword'),
             type = factor(type,
                           levels = c('non-iconic \nword', 'iconic \nword')))

Let’s check the count of words by itself:

# Save the word counts:

word_counts <- df |>
  count(type, word, sort = TRUE)

# Show:

word_counts |>
  print(n = Inf)

## # A tibble: 45 × 3
##    type                word          n
##    <fct>               <chr>     <int>
##  1 "non-iconic \nword" said        303
##  2 "iconic \nword"     spank        97
##  3 "iconic \nword"     slushy       67
##  4 "non-iconic \nword" realize      58
##  5 "non-iconic \nword" inform       57
##  6 "non-iconic \nword" wearing      56
##  7 "iconic \nword"     yucky        56
##  8 "non-iconic \nword" knew         54
##  9 "non-iconic \nword" filling      51
## 10 "non-iconic \nword" other        50
## 11 "non-iconic \nword" exact        46
## 12 "non-iconic \nword" grateful     43
## 13 "non-iconic \nword" prevail      40
## 14 "iconic \nword"     squish       37
## 15 "non-iconic \nword" tamper       36
## 16 "iconic \nword"     splotch      36
## 17 "non-iconic \nword" put          35
## 18 "non-iconic \nword" confirmed    34
## 19 "non-iconic \nword" rejoin       34
## 20 "non-iconic \nword" discern      32
## 21 "non-iconic \nword" jealous      30
## 22 "iconic \nword"     puffy        24
## 23 "non-iconic \nword" covet        22
## 24 "non-iconic \nword" ordain       21
## 25 "iconic \nword"     swish        21
## 26 "iconic \nword"     wring        21
## 27 "iconic \nword"     saggy        17
## 28 "iconic \nword"     swoosh       15
## 29 "iconic \nword"     zap          15
## 30 "non-iconic \nword" outwit       14
## 31 "iconic \nword"     chomp        14
## 32 "iconic \nword"     crispy       14
## 33 "non-iconic \nword" absent       13
## 34 "iconic \nword"     wheeze       13
## 35 "iconic \nword"     woof         13
## 36 "non-iconic \nword" sullen       11
## 37 "iconic \nword"     barking      11
## 38 "non-iconic \nword" acquaint      8
## 39 "iconic \nword"     bang          6
## 40 "iconic \nword"     munch         5
## 41 "iconic \nword"     plump         5
## 42 "iconic \nword"     wobbly        5
## 43 "non-iconic \nword" barren        3
## 44 "iconic \nword"     snap          2
## 45 "iconic \nword"     gooey         1

Create a non_iconic_gesture variable which is gesture minus iconic_gesture… this variable then specifically looks at all the cases of gestures that are not iconic.

# Seed with NA values:

df$non_iconic_gesture <- NA

# Create variable:

df <- mutate(df,
             non_iconic_gesture = case_when(gesture == 1 & iconic_gesture == 0 ~ 'gesture (non-iconic)',
                                            gesture == 0 & iconic_gesture == 0 ~ 'no gesture'))

# Double check:

df |> 
  distinct(gesture, iconic_gesture, non_iconic_gesture) |> 
  select(gesture, iconic_gesture, non_iconic_gesture)

## # A tibble: 4 × 3
##   gesture iconic_gesture non_iconic_gesture  
##     <dbl>          <dbl> <chr>               
## 1       1              0 gesture (non-iconic)
## 2       0              0 no gesture          
## 3       1              1 <NA>                
## 4       1             NA <NA>

That’s correct.

4 Descriptive statistics

Let’s count the overall average gesture rate:

# Save:

gesture_counts <- df |> 
  count(gesture) |> 
  mutate(proportion = n / sum(n))

# Show:

gesture_counts

## # A tibble: 2 × 3
##   gesture     n proportion
##     <dbl> <int>      <dbl>
## 1       0   664      0.429
## 2       1   882      0.571

Let’s count iconic gestures:

# Save:

iconic_counts <- df |> 
  filter(gesture == 1) |> 
  count(iconic_gesture) |> 
  mutate(proportion = n / sum(n))

# Show:

iconic_counts

## # A tibble: 3 × 3
##   iconic_gesture     n proportion
##            <dbl> <int>      <dbl>
## 1              0   671    0.761  
## 2              1   210    0.238  
## 3             NA     1    0.00113

Let’s count the overall gestures by word type:

# Save:

gesture_by_type_counts <- df |> 
  count(type, gesture) |> 
  group_by(type) |> 
  mutate(proportion = n / sum(n))

# Show:

gesture_by_type_counts

## # A tibble: 4 × 4
## # Groups:   type [2]
##   type                gesture     n proportion
##   <fct>                 <dbl> <int>      <dbl>
## 1 "non-iconic \nword"       0   514      0.489
## 2 "non-iconic \nword"       1   537      0.511
## 3 "iconic \nword"           0   150      0.303
## 4 "iconic \nword"           1   345      0.697

Let’s count the iconic gestures by word type:

# Save:

iconic_by_type_counts <- df |> 
  filter(gesture == 1) |> 
  count(type, iconic_gesture) |> 
  group_by(type) |> 
  mutate(proportion = n / sum(n))

# Show:

iconic_by_type_counts

## # A tibble: 5 × 4
## # Groups:   type [2]
##   type                iconic_gesture     n proportion
##   <fct>                        <dbl> <int>      <dbl>
## 1 "non-iconic \nword"              0   435    0.810  
## 2 "non-iconic \nword"              1   101    0.188  
## 3 "non-iconic \nword"             NA     1    0.00186
## 4 "iconic \nword"                  0   236    0.684  
## 5 "iconic \nword"                  1   109    0.316

Let’s do the same again, but this time only for those that are not iconic gestures.

# Save:

other_by_type_counts <- df |> 
  count(type, non_iconic_gesture) |> 
  filter(!is.na(non_iconic_gesture)) |> 
  group_by(type) |> 
  mutate(proportion = n / sum(n))

# Show:

other_by_type_counts

## # A tibble: 4 × 4
## # Groups:   type [2]
##   type                non_iconic_gesture       n proportion
##   <fct>               <chr>                <int>      <dbl>
## 1 "non-iconic \nword" gesture (non-iconic)   435      0.458
## 2 "non-iconic \nword" no gesture             514      0.542
## 3 "iconic \nword"     gesture (non-iconic)   236      0.611
## 4 "iconic \nword"     no gesture             150      0.389

Let’s do both of these things on a word by word basis. Gesture counts first:

# Save counts:

word_gesture_rates <- df |> 
  count(word, gesture) |> 
  group_by(word) |> 
  mutate(proportion = n / sum(n)) |> 
  filter(gesture == 1) |> 
  select(-gesture, -n)

# Show:

word_gesture_rates |> 
  arrange(desc(proportion)) |> 
  print(n = Inf)

## # A tibble: 44 × 2
## # Groups:   word [44]
##    word      proportion
##    <chr>          <dbl>
##  1 bang          1     
##  2 snap          1     
##  3 splotch       0.944 
##  4 chomp         0.929 
##  5 squish        0.892 
##  6 zap           0.867 
##  7 exact         0.826 
##  8 wring         0.810 
##  9 plump         0.8   
## 10 wobbly        0.8   
## 11 filling       0.784 
## 12 discern       0.781 
## 13 put           0.771 
## 14 ordain        0.762 
## 15 slushy        0.731 
## 16 crispy        0.714 
## 17 swish         0.714 
## 18 wearing       0.714 
## 19 spank         0.691 
## 20 barren        0.667 
## 21 swoosh        0.667 
## 22 other         0.66  
## 23 tamper        0.639 
## 24 barking       0.636 
## 25 covet         0.636 
## 26 acquaint      0.625 
## 27 woof          0.615 
## 28 realize       0.603 
## 29 munch         0.6   
## 30 knew          0.593 
## 31 outwit        0.571 
## 32 puffy         0.542 
## 33 rejoin        0.5   
## 34 confirmed     0.471 
## 35 jealous       0.467 
## 36 yucky         0.464 
## 37 sullen        0.455 
## 38 wheeze        0.385 
## 39 said          0.366 
## 40 saggy         0.353 
## 41 prevail       0.35  
## 42 grateful      0.279 
## 43 inform        0.158 
## 44 absent        0.0769

Proportion of iconic gestures (out of videos with gesture) by word:

# Save counts:

word_iconic_gesture_rates <- df |> 
  count(word, iconic_gesture) |> 
  group_by(word) |> 
  mutate(proportion = n / sum(n)) |> 
  filter(iconic_gesture == 1) |> 
  select(-iconic_gesture, -n)

# Show:

word_iconic_gesture_rates |> 
  arrange(desc(proportion)) |> 
  print(n = Inf)

## # A tibble: 35 × 2
## # Groups:   word [35]
##    word      proportion
##    <chr>          <dbl>
##  1 bang          0.833 
##  2 squish        0.811 
##  3 wobbly        0.6   
##  4 wring         0.524 
##  5 put           0.429 
##  6 woof          0.385 
##  7 chomp         0.357 
##  8 barren        0.333 
##  9 zap           0.333 
## 10 swish         0.286 
## 11 splotch       0.278 
## 12 tamper        0.222 
## 13 discern       0.219 
## 14 exact         0.217 
## 15 munch         0.2   
## 16 other         0.18  
## 17 filling       0.137 
## 18 swoosh        0.133 
## 19 spank         0.124 
## 20 slushy        0.119 
## 21 inform        0.105 
## 22 jealous       0.1   
## 23 covet         0.0909
## 24 puffy         0.0833
## 25 wheeze        0.0769
## 26 knew          0.0741
## 27 crispy        0.0714
## 28 outwit        0.0714
## 29 realize       0.0690
## 30 confirmed     0.0588
## 31 rejoin        0.0588
## 32 wearing       0.0536
## 33 said          0.0495
## 34 grateful      0.0465
## 35 yucky         0.0357

Proportion of other gestures (out of all videos, excluding non-iconic gestures) by word:

# Save counts:

other_gesture_rates <- df |> 
  count(word, non_iconic_gesture) |> 
  group_by(word) |> 
  mutate(proportion = n / sum(n)) |> 
  filter(non_iconic_gesture == 'gesture (non-iconic)') |> 
  select(-non_iconic_gesture, -n)

# Show:

other_gesture_rates |> 
  arrange(desc(proportion)) |> 
  print(n = Inf)

## # A tibble: 44 × 2
## # Groups:   word [44]
##    word      proportion
##    <chr>          <dbl>
##  1 snap          1     
##  2 plump         0.8   
##  3 ordain        0.762 
##  4 splotch       0.667 
##  5 wearing       0.661 
##  6 filling       0.647 
##  7 crispy        0.643 
##  8 barking       0.636 
##  9 acquaint      0.625 
## 10 slushy        0.612 
## 11 exact         0.609 
## 12 chomp         0.571 
## 13 spank         0.567 
## 14 discern       0.562 
## 15 covet         0.545 
## 16 swoosh        0.533 
## 17 zap           0.533 
## 18 knew          0.519 
## 19 realize       0.517 
## 20 outwit        0.5   
## 21 other         0.48  
## 22 puffy         0.458 
## 23 sullen        0.455 
## 24 rejoin        0.441 
## 25 swish         0.429 
## 26 yucky         0.429 
## 27 tamper        0.417 
## 28 confirmed     0.412 
## 29 munch         0.4   
## 30 jealous       0.367 
## 31 saggy         0.353 
## 32 prevail       0.35  
## 33 put           0.343 
## 34 barren        0.333 
## 35 said          0.317 
## 36 wheeze        0.308 
## 37 wring         0.286 
## 38 grateful      0.233 
## 39 woof          0.231 
## 40 wobbly        0.2   
## 41 bang          0.167 
## 42 squish        0.0811
## 43 absent        0.0769
## 44 inform        0.0526

Let’s merge the counts and the proportions into a big table showing everything on a by-word basis:

# Save:

by_word_all <- left_join(word_counts, word_gesture_rates) |> 
  rename(gesture_proportion = proportion) |> 
  left_join(word_iconic_gesture_rates) |> 
  rename(iconic_gesture_proportion = proportion) |> 
  left_join(other_gesture_rates) |> 
  rename(other_proportion = proportion) |> 
  mutate(type = str_replace(type, '\n', ''),
         type = factor(type, levels = c('non-iconic word', 'iconic word')))

## Joining with `by = join_by(word)`
## Joining with `by = join_by(word)`
## Joining with `by = join_by(word)`

# Show:

by_word_all |> 
  print(n = Inf)

## # A tibble: 45 × 6
##    type   word      n gesture_proportion iconic_gesture_propo…¹ other_proportion
##    <fct>  <chr> <int>              <dbl>                  <dbl>            <dbl>
##  1 non-i… said    303             0.366                  0.0495           0.317 
##  2 iconi… spank    97             0.691                  0.124            0.567 
##  3 iconi… slus…    67             0.731                  0.119            0.612 
##  4 non-i… real…    58             0.603                  0.0690           0.517 
##  5 non-i… info…    57             0.158                  0.105            0.0526
##  6 non-i… wear…    56             0.714                  0.0536           0.661 
##  7 iconi… yucky    56             0.464                  0.0357           0.429 
##  8 non-i… knew     54             0.593                  0.0741           0.519 
##  9 non-i… fill…    51             0.784                  0.137            0.647 
## 10 non-i… other    50             0.66                   0.18             0.48  
## 11 non-i… exact    46             0.826                  0.217            0.609 
## 12 non-i… grat…    43             0.279                  0.0465           0.233 
## 13 non-i… prev…    40             0.35                  NA                0.35  
## 14 iconi… squi…    37             0.892                  0.811            0.0811
## 15 non-i… tamp…    36             0.639                  0.222            0.417 
## 16 iconi… splo…    36             0.944                  0.278            0.667 
## 17 non-i… put      35             0.771                  0.429            0.343 
## 18 non-i… conf…    34             0.471                  0.0588           0.412 
## 19 non-i… rejo…    34             0.5                    0.0588           0.441 
## 20 non-i… disc…    32             0.781                  0.219            0.562 
## 21 non-i… jeal…    30             0.467                  0.1              0.367 
## 22 iconi… puffy    24             0.542                  0.0833           0.458 
## 23 non-i… covet    22             0.636                  0.0909           0.545 
## 24 non-i… orda…    21             0.762                 NA                0.762 
## 25 iconi… swish    21             0.714                  0.286            0.429 
## 26 iconi… wring    21             0.810                  0.524            0.286 
## 27 iconi… saggy    17             0.353                 NA                0.353 
## 28 iconi… swoo…    15             0.667                  0.133            0.533 
## 29 iconi… zap      15             0.867                  0.333            0.533 
## 30 non-i… outw…    14             0.571                  0.0714           0.5   
## 31 iconi… chomp    14             0.929                  0.357            0.571 
## 32 iconi… cris…    14             0.714                  0.0714           0.643 
## 33 non-i… abse…    13             0.0769                NA                0.0769
## 34 iconi… whee…    13             0.385                  0.0769           0.308 
## 35 iconi… woof     13             0.615                  0.385            0.231 
## 36 non-i… sull…    11             0.455                 NA                0.455 
## 37 iconi… bark…    11             0.636                 NA                0.636 
## 38 non-i… acqu…     8             0.625                 NA                0.625 
## 39 iconi… bang      6             1                      0.833            0.167 
## 40 iconi… munch     5             0.6                    0.2              0.4   
## 41 iconi… plump     5             0.8                   NA                0.8   
## 42 iconi… wobb…     5             0.8                    0.6              0.2   
## 43 non-i… barr…     3             0.667                  0.333            0.333 
## 44 iconi… snap      2             1                     NA                1     
## 45 iconi… gooey     1            NA                     NA               NA     
## # ℹ abbreviated name: ¹​iconic_gesture_proportion

The NA’s in this table are true zeros, so they should be replaced with 0 proportion.

by_word_all <- mutate(by_word_all,
                      gesture_proportion = ifelse(is.na(gesture_proportion),
                                                  0, gesture_proportion),
                      iconic_gesture_proportion = ifelse(is.na(iconic_gesture_proportion),
                                                         0, iconic_gesture_proportion),
                      other_proportion = ifelse(is.na(other_proportion),
                                                0, other_proportion))

# Show again:

by_word_all |> 
  print(n = Inf)

## # A tibble: 45 × 6
##    type   word      n gesture_proportion iconic_gesture_propo…¹ other_proportion
##    <fct>  <chr> <int>              <dbl>                  <dbl>            <dbl>
##  1 non-i… said    303             0.366                  0.0495           0.317 
##  2 iconi… spank    97             0.691                  0.124            0.567 
##  3 iconi… slus…    67             0.731                  0.119            0.612 
##  4 non-i… real…    58             0.603                  0.0690           0.517 
##  5 non-i… info…    57             0.158                  0.105            0.0526
##  6 non-i… wear…    56             0.714                  0.0536           0.661 
##  7 iconi… yucky    56             0.464                  0.0357           0.429 
##  8 non-i… knew     54             0.593                  0.0741           0.519 
##  9 non-i… fill…    51             0.784                  0.137            0.647 
## 10 non-i… other    50             0.66                   0.18             0.48  
## 11 non-i… exact    46             0.826                  0.217            0.609 
## 12 non-i… grat…    43             0.279                  0.0465           0.233 
## 13 non-i… prev…    40             0.35                   0                0.35  
## 14 iconi… squi…    37             0.892                  0.811            0.0811
## 15 non-i… tamp…    36             0.639                  0.222            0.417 
## 16 iconi… splo…    36             0.944                  0.278            0.667 
## 17 non-i… put      35             0.771                  0.429            0.343 
## 18 non-i… conf…    34             0.471                  0.0588           0.412 
## 19 non-i… rejo…    34             0.5                    0.0588           0.441 
## 20 non-i… disc…    32             0.781                  0.219            0.562 
## 21 non-i… jeal…    30             0.467                  0.1              0.367 
## 22 iconi… puffy    24             0.542                  0.0833           0.458 
## 23 non-i… covet    22             0.636                  0.0909           0.545 
## 24 non-i… orda…    21             0.762                  0                0.762 
## 25 iconi… swish    21             0.714                  0.286            0.429 
## 26 iconi… wring    21             0.810                  0.524            0.286 
## 27 iconi… saggy    17             0.353                  0                0.353 
## 28 iconi… swoo…    15             0.667                  0.133            0.533 
## 29 iconi… zap      15             0.867                  0.333            0.533 
## 30 non-i… outw…    14             0.571                  0.0714           0.5   
## 31 iconi… chomp    14             0.929                  0.357            0.571 
## 32 iconi… cris…    14             0.714                  0.0714           0.643 
## 33 non-i… abse…    13             0.0769                 0                0.0769
## 34 iconi… whee…    13             0.385                  0.0769           0.308 
## 35 iconi… woof     13             0.615                  0.385            0.231 
## 36 non-i… sull…    11             0.455                  0                0.455 
## 37 iconi… bark…    11             0.636                  0                0.636 
## 38 non-i… acqu…     8             0.625                  0                0.625 
## 39 iconi… bang      6             1                      0.833            0.167 
## 40 iconi… munch     5             0.6                    0.2              0.4   
## 41 iconi… plump     5             0.8                    0                0.8   
## 42 iconi… wobb…     5             0.8                    0.6              0.2   
## 43 non-i… barr…     3             0.667                  0.333            0.333 
## 44 iconi… snap      2             1                      0                1     
## 45 iconi… gooey     1             0                      0                0     
## # ℹ abbreviated name: ¹​iconic_gesture_proportion

# Save outside of R:

by_word_all |> 
  write_csv('../data/by_word_proportions.csv')

5 Data visualization

Let’s make a bar plot of the gesture counts:

# Basic plot:

gesture_p <- gesture_by_type_counts |> 
  mutate(gesture = ifelse(gesture == 1, 'gesture', 'no gesture')) |> 
  mutate(gesture = factor(gesture,
                          levels = c('no gesture', 'gesture'))) |> 
  ggplot(aes(x = type,
             y = proportion,
             fill = gesture)) +
  geom_col(width = 0.55)

# Axes and labels:

gesture_p <- gesture_p +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  scale_y_continuous(expand = c(0, 0)) +
  xlab(NULL) +
  ylab('Proportion')

# Look and feel:

gesture_p <- gesture_p +
  theme_classic()

# Show:

gesture_p

Same for iconic gestures only:

# Basic plot:

iconic_p <- iconic_by_type_counts |> 
  mutate(iconic_gesture = ifelse(iconic_gesture == 1,
                                 'iconic gesture',
                                 'other gesture')) |> 
  mutate(iconic_gesture = factor(iconic_gesture,
                                 levels = c('other gesture', 'iconic gesture'))) |> 
  ggplot(aes(x = type,
             y = proportion,
             fill = iconic_gesture)) +
  geom_col(width = 0.55)

# Axes and labels:

iconic_p <- iconic_p +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  scale_y_continuous(expand = c(0, 0)) +
  xlab(NULL) +
  ylab('Proportion')

# Look and feel:

iconic_p <- iconic_p +
  theme_classic()

# Show:

iconic_p

Same for other types of gestures only. This will be the rightmost plot in our multiple plot array. For this reason we change the variable to the levels yes and no because then those levels can serve as legend for all three plots (yes gesture vs. no gesture, yes iconic versus no iconic etc.)

# Basic plot:

other_p <- other_by_type_counts |> 
  mutate(non_iconic_gesture = ifelse(non_iconic_gesture == 'no gesture',
                                     'no', 'yes'),
         non_iconic_gesture = factor(non_iconic_gesture,
                                     levels = c('no', 'yes'))) |> 
  ggplot(aes(x = type,
             y = proportion,
             fill = non_iconic_gesture)) +
  geom_col(width = 0.55)

# Axes and labels:

other_p <- other_p +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  scale_y_continuous(expand = c(0, 0)) +
  xlab(NULL) +
  ylab('Proportion')

# Look and feel:

other_p <- other_p +
  theme_classic()

# Show:

other_p

Put them all into a three-column plot array, using the patchwork library. But we should then also

# Add titles and switch off legends except for the last one:

gesture_p <- gesture_p +
  ggtitle('a) All gestures') +
  theme(legend.position = 'none',
        plot.caption = element_text(hjust = 0))

iconic_p <- iconic_p +
  ggtitle('b) Iconic gestures') +
  theme(legend.position = 'none',
        plot.caption = element_text(hjust = 0)) +
  ylab(NULL)

other_p <- other_p +
  ggtitle('c) Other gestures') +
  ylab(NULL) +
  theme(plot.caption = element_text(hjust = 0))

# Combine:

three_p <- gesture_p + iconic_p + other_p +
  plot_layout(ncol = 3)

# Save combined plot outside:

ggsave(plot = three_p, filename = '../figures/barplots.pdf',
       width = 7, height = 3.5)

Let’s make a density plot out of this, gesture_proportion:

# Plot basics:

ges_prop_p <- by_word_all |> 
  ggplot(aes(x = gesture_proportion, fill = type)) +
  geom_density(alpha = 0.5)

# Axes and labels:

ges_prop_p <- ges_prop_p +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 3),
                     breaks = seq(0, 3, 0.5)) +
  scale_x_continuous(expand = c(0, 0),
                     limits = c(0, 1),
                     breaks = seq(0, 1, 0.25)) +
  xlab('Gesture proportion of each word') +
  ylab('Density')

# Themes:

ges_prop_p <- ges_prop_p +
  theme_classic() +
  theme(legend.position = 'bottom') +
  ggtitle('a) Proportion of all gestures\nacross words')

# Show:

ges_prop_p

Let’s make a density plot out of this, gesture_proportion:

# Plot basics:

icon_prop_p <- by_word_all |> 
  ggplot(aes(x = iconic_gesture_proportion, fill = type)) +
  geom_density(alpha = 0.5)

# Axes and labels:

icon_prop_p <- icon_prop_p +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 3),
                     breaks = seq(0, 3, 0.5)) +
  scale_x_continuous(expand = c(0, 0),
                     limits = c(0, 1),
                     breaks = seq(0, 1, 0.25)) +
  xlab('Iconic gesture proportion of each word') +
  ylab('Density')

# Themes:

icon_prop_p <- icon_prop_p +
  theme_classic() +
  theme(legend.position = 'bottom') +
  ggtitle('b) Proportion of iconic gestures\nacross words')

# Show:

icon_prop_p

Proportion of other gestures:

# Plot basics:

other_prop_p <- by_word_all |> 
  ggplot(aes(x = other_proportion, fill = type)) +
  geom_density(alpha = 0.5)

# Axes and labels:

other_prop_p <- other_prop_p +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 3),
                     breaks = seq(0, 3, 0.5)) +
  scale_x_continuous(expand = c(0, 0),
                     limits = c(0, 1),
                     breaks = seq(0, 1, 0.25)) +
  xlab('Other gesture proportion of each word') +
  ylab('Density')

# Themes:

other_prop_p <- other_prop_p +
  theme_classic() +
  theme(legend.position = 'bottom') +
  ggtitle('c) Proportion of any other gestures\nacross words')

# Show:

other_prop_p

Put all three density plots into one big plot:

# Add titles and switch off legends except for the last one:

ges_prop_p <- ges_prop_p +
  theme(legend.position = 'none',
        plot.caption = element_text(hjust = 0))

icon_prop_p <- icon_prop_p +
  theme(legend.position = 'none',
        plot.caption = element_text(hjust = 0)) +
  ylab(NULL)

other_prop_p <- other_prop_p +
  ylab(NULL) +
  theme(plot.caption = element_text(hjust = 0))

# Combine:

three_prop_p <- ges_prop_p + icon_prop_p + other_prop_p +
  plot_layout(ncol = 3)

# Save combined plot outside:

ggsave(plot = three_prop_p, filename = '../figures/density_plots.pdf',
       width = 12, height = 3.5)

Let’s see whether we can do a bar plot of all the words for gesture_proportion:

# Plot basics:

word_bars_p <- by_word_all |> 
  ggplot(aes(x = reorder(word, gesture_proportion),
             y = gesture_proportion, fill = type)) +
  geom_col(width = 0.75) +
  geom_text(aes(label = n),
            nudge_y = +0.025,
            size = 2.7)

# Axes and labels:

word_bars_p <- word_bars_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.1)) +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  ylab('Proportion of videos with gesture') +
  xlab(NULL)

# Look and feel:

word_bars_p <- word_bars_p +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1),
        legend.position = 'bottom')

# Show:

word_bars_p

# Save:

ggsave(plot = word_bars_p, filename = '../figures/by_word_bars.pdf',
       width = 10, height = 4)

Same for iconic_gesture_proportion:

# Plot basics:

iconic_bars_p <- by_word_all |> 
  ggplot(aes(x = reorder(word, iconic_gesture_proportion),
             y = iconic_gesture_proportion, fill = type)) +
  geom_col(width = 0.75) +
  geom_text(aes(label = n),
            nudge_y = +0.025,
            size = 2.7)

# Axes and labels:

iconic_bars_p <- iconic_bars_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.1)) +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  ylab('Proportion of gestures that are iconic') +
  xlab(NULL)

# Look and feel:

iconic_bars_p <- iconic_bars_p +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1),
        legend.position = 'bottom')

# Show:

iconic_bars_p

# Save:

ggsave(plot = iconic_bars_p, filename = '../figures/by_word_iconic_bars.pdf',
       width = 10, height = 4)

Same for other:

Same for iconic_gesture_proportion:

# Plot basics:

other_bars_p <- by_word_all |> 
  ggplot(aes(x = reorder(word, other_proportion),
             y = other_proportion, fill = type)) +
  geom_col(width = 0.75) +
  geom_text(aes(label = n),
            nudge_y = +0.025,
            size = 2.7)

# Axes and labels:

other_bars_p <- other_bars_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.1)) +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  ylab('Proportion of videos with non-iconic gestures') +
  xlab(NULL)

# Look and feel:

other_bars_p <- other_bars_p +
  theme_classic() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1),
        legend.position = 'bottom')

# Show:

other_bars_p

# Save:

ggsave(plot = other_bars_p, filename = '../figures/by_word_other_bars.pdf',
       width = 10, height = 4)

6 Inferential statistics

6.1 Build models

Specify weakly informative priors, specifically for the beta coefficient, using the recommendation by Gelman et al. (2008) to specify a Cauchy prior centered at 0 with scale 2.5.

weak_priors <- c(prior(student_t(3, 0, 2.5), class = Intercept),
                 prior(student_t(3, 0, 2.5), class = sd),
                 prior(cauchy(0, 2.5), class = b)) # Gelman et al. (2008)

Let’s fit a model with a fixed effect of type, and random intercepts for word and url because we have multiple data points for each of these grouping factors. We cannot fit type random slopes here because there is no possible variation whatsoever of type within word or url since each word or video is always either iconic or not iconic.

gesture_mdl <- brm(gesture ~
                     
                     # Fixed effects:
                     
                     1 + type +
                     
                     # Random effects:
                     
                     (1|word) + (1|url),
                   
                   # More model specs:
                   
                   prior = weak_priors,
                   family = bernoulli,
                   data = df,
                   
                   # MCMC estimation specs:
                   
                   seed = 42, cores = 4,
                   iter = 4000, warmup = 2000)

# Save:

save(gesture_mdl, file = '../models/gesture_mdl.RData')

Load and show model:

# Load:

load('../models/gesture_mdl.Rdata')

## Warning: namespace 'diffobj' is not available and has been replaced
## by .GlobalEnv when processing object 'gesture_mdl'

# Show:

gesture_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: gesture ~ 1 + type + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1545) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 836) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.25      0.26     1.79     2.79 1.00     2051     3825
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.30      0.24     0.90     1.82 1.00     3637     5289
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept            0.58      0.32    -0.05     1.22 1.00     4680     5344
## typeiconicDnword     0.92      0.48    -0.00     1.90 1.00     5714     5475
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Show the priors just to double check:

prior_summary(gesture_mdl)

##                 prior     class             coef group resp dpar nlpar lb ub
##        cauchy(0, 2.5)         b                                             
##        cauchy(0, 2.5)         b typeiconicDnword                            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5)        sd                                         0   
##  student_t(3, 0, 2.5)        sd                    url                  0   
##  student_t(3, 0, 2.5)        sd        Intercept   url                  0   
##  student_t(3, 0, 2.5)        sd                   word                  0   
##  student_t(3, 0, 2.5)        sd        Intercept  word                  0   
##        source
##          user
##  (vectorized)
##          user
##          user
##  (vectorized)
##  (vectorized)
##  (vectorized)
##  (vectorized)

Show the posterior:

gesture_mdl_posts <- posterior_samples(gesture_mdl)

## Warning: Method 'posterior_samples' is deprecated. Please see ?as_draws for
## recommended alternatives.

Make a plot of the posterior distribution of the type coefficient:

# Plot basics:

gesture_posts_p <- gesture_mdl_posts |> 
  ggplot(aes(x = b_typeiconicDnword)) +
  geom_density(fill = 'purple3') +
  geom_vline(xintercept = 0, linetype = 'dashed')

# Axes and labels:

gesture_posts_p <- gesture_posts_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.2),
                     breaks = seq(0, 1.2, 0.2)) +
  scale_x_continuous(limits = c(-3, 3),
                     breaks = seq(-3, 3, 1))

# Look and feel:

gesture_posts_p <- gesture_posts_p +
  ylab('Density of posterior samples') +
  xlab('Posterior estimate of coefficient') +
  theme_classic()

# Show and save:

gesture_posts_p

ggsave(plot = gesture_posts_p, filename = '../figures/gesture_posterior.pdf',
       width = 4.7, height = 3)

This shows that given the model formula, prior, and data, most of the plausible type effects are positive, which means that it is more plausible that iconic words also co-occur with gesture. Since the posterior distribution crosses over zero, it is possible that the effect could be negative, but this is quite improbable given where the bulk of the posterior distribution lies.

This is to calculate the actual posterior probability of the effect being positive (= of the same sign), which is essentially just pinning a number to what proportion of the area in the distribution above is to the right of the dashed line.

hypothesis(gesture_mdl, 'typeiconicDnword > 0')

## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (typeiconicDnword) > 0     0.92      0.48     0.15     1.73       38.8
##   Post.Prob Star
## 1      0.97    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Same for iconic gestures:

iconic_mdl <- brm(iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = df,
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(iconic_mdl, file = '../models/iconic_mdl.RData')

Load and show model:

# Load model:

load('../models/iconic_mdl.RData')

## Warning: namespace 'diffobj' is not available and has been replaced
## by .GlobalEnv when processing object 'iconic_mdl'

# Show model:

iconic_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: iconic_gesture ~ 1 + type + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1545) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 836) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.19      0.33     1.60     2.90 1.00     1841     2843
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.68      0.33     1.14     2.42 1.00     2807     4487
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           -3.86      0.55    -5.03    -2.89 1.00     2845     4072
## typeiconicDnword     1.49      0.63     0.30     2.79 1.00     4142     4521
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Show the priors to double-check:

prior_summary(iconic_mdl)

##                 prior     class             coef group resp dpar nlpar lb ub
##        cauchy(0, 2.5)         b                                             
##        cauchy(0, 2.5)         b typeiconicDnword                            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5)        sd                                         0   
##  student_t(3, 0, 2.5)        sd                    url                  0   
##  student_t(3, 0, 2.5)        sd        Intercept   url                  0   
##  student_t(3, 0, 2.5)        sd                   word                  0   
##  student_t(3, 0, 2.5)        sd        Intercept  word                  0   
##        source
##          user
##  (vectorized)
##          user
##          user
##  (vectorized)
##  (vectorized)
##  (vectorized)
##  (vectorized)

Show the posterior of the type coefficient. First, extract the posterior samples:

iconic_mdl_posts <- posterior_samples(iconic_mdl)

## Warning: Method 'posterior_samples' is deprecated. Please see ?as_draws for
## recommended alternatives.

Make a plot of the posterior distribution of the coefficient:

# Plot basics:

iconic_posts_p <- iconic_mdl_posts |> 
  ggplot(aes(x = b_typeiconicDnword)) +
  geom_density(fill = 'purple3') +
  geom_vline(xintercept = 0, linetype = 'dashed')

# Axes and labels:

iconic_posts_p <- iconic_posts_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.2),
                     breaks = seq(0, 1.2, 0.2)) +
  scale_x_continuous(limits = c(-3, 3),
                     breaks = seq(-3, 3, 1))

# Look and feel:

iconic_posts_p <- iconic_posts_p +
  ylab('Density of posterior samples') +
  xlab('Posterior estimate of coefficient') +
  theme_classic()

# Show and save:

iconic_posts_p

## Warning: Removed 93 rows containing non-finite outside the scale range
## (`stat_density()`).

ggsave(plot = iconic_posts_p, filename = '../figures/iconic_gesture_posterior.pdf',
       width = 4.7, height = 3)

## Warning: Removed 93 rows containing non-finite outside the scale range
## (`stat_density()`).

Check whether the main effect of iconicity is likely to be of the same sign. This is the posterior probability of iconic words having a higher gesture rate:

hypothesis(iconic_mdl, 'typeiconicDnword > 0')

## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (typeiconicDnword) > 0     1.49      0.63     0.49     2.55     130.15
##   Post.Prob Star
## 1      0.99    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

The final model is the one with only the non-iconic gestures:

Same for non-iconic (= “other”) gestures:

other_mdl <- brm(non_iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = filter(df, !is.na(non_iconic_gesture)),
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(other_mdl, file = '../models/other_mdl.RData')

Load and show model:

# Load model:

load('../models/other_mdl.RData')

## Warning: namespace 'diffobj' is not available and has been replaced
## by .GlobalEnv when processing object 'other_mdl'

# Show model:

other_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: non_iconic_gesture ~ 1 + type + (1 | word) + (1 | url) 
##    Data: filter(df, !is.na(non_iconic_gesture)) (Number of observations: 1332) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 732) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.34      0.29     1.83     2.96 1.00     1773     3551
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.21      0.24     0.80     1.73 1.00     3068     5288
## 
## Regression Coefficients:
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           -0.25      0.31    -0.85     0.36 1.00     5376     5336
## typeiconicDnword    -0.46      0.48    -1.40     0.46 1.00     6371     4653
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Show the priors to double-check:

prior_summary(other_mdl)

##                 prior     class             coef group resp dpar nlpar lb ub
##        cauchy(0, 2.5)         b                                             
##        cauchy(0, 2.5)         b typeiconicDnword                            
##  student_t(3, 0, 2.5) Intercept                                             
##  student_t(3, 0, 2.5)        sd                                         0   
##  student_t(3, 0, 2.5)        sd                    url                  0   
##  student_t(3, 0, 2.5)        sd        Intercept   url                  0   
##  student_t(3, 0, 2.5)        sd                   word                  0   
##  student_t(3, 0, 2.5)        sd        Intercept  word                  0   
##        source
##          user
##  (vectorized)
##          user
##          user
##  (vectorized)
##  (vectorized)
##  (vectorized)
##  (vectorized)

Show the posterior of the type coefficient. First, extract the posterior samples:

other_mdl_posts <- posterior_samples(other_mdl)

## Warning: Method 'posterior_samples' is deprecated. Please see ?as_draws for
## recommended alternatives.

Make a plot of the posterior distribution of the coefficient:

# Plot basics:

other_posts_p <- other_mdl_posts |> 
  ggplot(aes(x = b_typeiconicDnword)) +
  geom_density(fill = 'purple3') +
  geom_vline(xintercept = 0, linetype = 'dashed')

# Axes and labels:

other_posts_p <- other_posts_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.2),
                     breaks = seq(0, 1.2, 0.2)) +
  scale_x_continuous(limits = c(-3, 3),
                     breaks = seq(-3, 3, 1))

# Look and feel:

other_posts_p <- other_posts_p +
  ylab('Density of posterior samples') +
  xlab('Posterior estimate of coefficient') +
  theme_classic()

# Show and save:

other_posts_p

ggsave(plot = other_posts_p, filename = '../figures/other_gesture_posterior.pdf',
       width = 4.7, height = 3)

Check how many of them are of the same sign:

hypothesis(other_mdl, 'typeiconicDnword < 0')

## Hypothesis Tests for class b:
##               Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (typeiconicDnword) < 0    -0.46      0.48    -1.25     0.31       4.92
##   Post.Prob Star
## 1      0.83     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

6.2 Posterior predictive checks

To assess whether the models make reasonable assumptions about the underlying data-generating processes, we can simulate new data.

Regular bar plots:

# Any gesture model:

pp_check(gesture_mdl, type = "bars", ndraws = 100)

# Iconic gesture model:

pp_check(iconic_mdl, type = "bars", ndraws = 100)

# Other gesture model:

pp_check(other_mdl, type = "bars", ndraws = 100)

Grouped bar plots:

# Any gesture model:

pp_check(gesture_mdl, type = "bars_grouped", ndraws = 100,
         group = 'word')

ggsave('../figures/gesture_mdl_pp_check.pdf',
       width = 14, height = 12)

# Iconic gesture model:

pp_check(iconic_mdl, type = "bars_grouped", ndraws = 100,
         group = 'word')

ggsave('../figures/iconic_mdl_pp_check.pdf',
       width = 14, height = 12)

# Other gesture model:

pp_check(other_mdl, type = "bars_grouped", ndraws = 100,
         group = 'word')

ggsave('../figures/other_mdl_pp_check.pdf',
       width = 14, height = 12)

ECDF (empirical cumulative distribution function):

# Any gesture model:

pp_check(gesture_mdl, type = "ecdf_overlay", ndraws = 100)

# Iconic gesture model:

pp_check(iconic_mdl, type = "ecdf_overlay", ndraws = 100)

# Other gesture model:

pp_check(other_mdl, type = "ecdf_overlay", ndraws = 100)

This completes this analysis.

7 Incorporating frequency and POS

7.1 Merge data into main data

As it has been found that frequency influences gesture production rates, let’s incorporate that:

# load, rename, and log-transform

SUBTL <- read_csv('../data/SUBTLEX_US_with_POS.csv') |> 
  rename(freq = FREQcount) |> 
  mutate(log_freq = log10(freq))

Merge this into by_word_all:

by_word_all <- left_join(by_word_all,
                         select(SUBTL, Word, freq, log_freq),
                         by = c('word' = 'Word'))

7.2 Descriptive statistics & data visualization

Are iconic words different from non-iconic ones in terms of frequency?

by_word_all |> 
  mutate(type = as.character(type),
         type = if_else(type == 'non-iconic word', 'minimally iconic\nword', 'highly iconic\nword'),
         type = factor(type, levels = c('minimally iconic\nword', 'highly iconic\nword'))) |> 
  ggplot(aes(x = type, y = log_freq, fill = type)) +
  geom_boxplot(width = 0.5) +
  scale_fill_manual(values = c('steelblue', 'goldenrod3'),
                    name = '') +
  xlab(NULL) +
  ylab('Log10 frequency') +
  scale_y_continuous(limits = c(0, 5)) +
  theme_classic() +
  theme(legend.position = 'none') +
  theme(axis.text.x = element_text(size = 10, face = 'bold'),
        axis.title.y = element_text(margin = margin(r = 15),
                                    size = 12, face = 'bold'))

ggsave(filename = '../figures/barplot_frequency_difference.pdf',
       width = 3.5, height = 4.2)

Looks like a big difference. Check the raw frequency and log frequency descriptive stats difference:

by_word_all |> 
  group_by(type) |> 
  summarize(freq_M = mean(freq, na.rm = TRUE),
            log_freq_M = mean(log_freq, na.rm = TRUE))

## # A tibble: 2 × 3
##   type            freq_M log_freq_M
##   <fct>            <dbl>      <dbl>
## 1 non-iconic word  7408.       2.64
## 2 iconic word       160.       1.76

Check how big this difference is in terms of effect size (Cohen’s d):

cohen.d(log_freq ~ type, data = by_word_all)

## 
## Cohen's d
## 
## d estimate: 0.9058493 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.2743632 1.5373355

Large effect size.

Quickly check whether frequency is correlated with any of the gesture rates, using Spearman’s rho, because these are proportions (but it doesn’t really matter, and Pearson’s r would be fine as well):

with(by_word_all, cor.test(log_freq, gesture_proportion, method = 'spearman'))

## Warning in cor.test.default(log_freq, gesture_proportion, method = "spearman"):
## Cannot compute exact p-value with ties

## 
##  Spearman's rank correlation rho
## 
## data:  log_freq and gesture_proportion
## S = 16678, p-value = 0.5191
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##         rho 
## -0.09865885

with(by_word_all, cor.test(log_freq, iconic_gesture_proportion, method = 'spearman'))

## Warning in cor.test.default(log_freq, iconic_gesture_proportion, method =
## "spearman"): Cannot compute exact p-value with ties

## 
##  Spearman's rank correlation rho
## 
## data:  log_freq and iconic_gesture_proportion
## S = 15267, p-value = 0.97
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##          rho 
## -0.005764155

with(by_word_all, cor.test(log_freq, other_proportion, method = 'spearman'))

## Warning in cor.test.default(log_freq, other_proportion, method = "spearman"):
## Cannot compute exact p-value with ties

## 
##  Spearman's rank correlation rho
## 
## data:  log_freq and other_proportion
## S = 17487, p-value = 0.3191
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.1519454

Perhaps Pearson’s r correlations are easier to interpret:

with(by_word_all, cor.test(log_freq, gesture_proportion, method = 'pearson'))

## 
##  Pearson's product-moment correlation
## 
## data:  log_freq and gesture_proportion
## t = -0.52008, df = 43, p-value = 0.6057
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3641455  0.2195670
## sample estimates:
##         cor 
## -0.07906252

with(by_word_all, cor.test(log_freq, iconic_gesture_proportion, method = 'pearson'))

## 
##  Pearson's product-moment correlation
## 
## data:  log_freq and iconic_gesture_proportion
## t = -0.075748, df = 43, p-value = 0.94
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3040537  0.2829425
## sample estimates:
##         cor 
## -0.01155072

with(by_word_all, cor.test(log_freq, other_proportion, method = 'pearson'))

## 
##  Pearson's product-moment correlation
## 
## data:  log_freq and other_proportion
## t = -0.5177, df = 43, p-value = 0.6073
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3638327  0.2199102
## sample estimates:
##         cor 
## -0.07870418

Not much of any correlations at all. I’d perhaps report these as these are really easy to understand by many people, making it clear that these are on by-word averages.

Make a plot of this, also incorporating word iconicity (type). For heuristic purposes we’ll also add a linear model to see whether we can spot any obvious relations that differ between iconic and non-iconic words:

by_word_all |> 
  ggplot(aes(x = log_freq, y = gesture_proportion,
             color = type, label = word)) +
  geom_text() +
  xlab('Log frequency') +
  ylab('Gesture proportion') +
  # geom_smooth(method = 'lm') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'),
                     name = '') +
  theme_classic() +
  theme(legend.position = 'bottom',
        axis.title = element_text(size = 12, face = 'bold'),
        axis.title.y = element_text(margin = margin(r = 15)),
        axis.title.x = element_text(margin = margin(t = 12)))

# Save:

ggsave('../figures/by_word_correlation_frequency_gesture_proportion.pdf',
       width = 6.5, height = 5)

The massive overlap and wide scatter suggests that there’s not much of a relation.

by_word_all |> 
  ggplot(aes(x = log_freq, y = iconic_gesture_proportion,
             color = type, label = word)) +
  geom_text() +
  xlab('Log frequency') +
  ylab('Iconic gesture proportion') +
  # geom_smooth(method = 'lm') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'),
                     name = '') +
  theme_classic() +
  theme(legend.position = 'bottom')

# Save:

ggsave('../figures/by_word_correlation_frequency_iconic_gesture_proportion.pdf',
       width = 6.5, height = 5)

Very weak positive relationship with more frequent words being more iconically gestured.

7.3 Frequency models

What happens if we incorporate frequency into the main analysis? For this we also need to add it to df:

df <- left_join(df, select(SUBTL, Word, freq, log_freq),
                by = c('word' = 'Word'))

The model has problems if type contains the paragraph break we included above for data viz purposes.

df <- mutate(df,
             type = as.character(type),
             type = ifelse(type == 'non-iconic \nword',
                           'non_iconic',
                           'iconic'),
             type = factor(type, levels = c('non_iconic', 'iconic')))

Check:

gesture_freq_mdl <- brm(gesture ~
                     
                     # Fixed effects:
                     
                     1 + type + log_freq +
                     
                     # Random effects:
                     
                     (1|word) + (1|url),
                   
                   # More model specs:
                   
                   prior = weak_priors,
                   family = bernoulli,
                   data = df,
                   
                   # MCMC estimation specs:
                   
                   seed = 42, cores = 4,
                   iter = 4000, warmup = 2000)

# Save:

save(gesture_freq_mdl, file = '../models/gesture_freq_mdl.RData')

Load:

load('../models/gesture_freq_mdl.RData')

Show model:

gesture_freq_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: gesture ~ 1 + type + log_freq + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1547) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 838) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.26      0.26     1.78     2.82 1.00     1868     3553
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.34      0.24     0.93     1.85 1.00     3349     5696
## 
## Regression Coefficients:
##            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept      0.52      0.76    -0.96     1.99 1.00     3893     4852
## typeiconic     0.95      0.55    -0.15     2.05 1.00     4460     4945
## log_freq       0.02      0.25    -0.46     0.51 1.00     3680     4673
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check effects:

hypothesis(gesture_freq_mdl, 'typeiconic > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (typeiconic) > 0     0.95      0.55     0.05     1.88      22.81      0.96
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_freq_mdl, 'log_freq > 0')

## Hypothesis Tests for class b:
##       Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (log_freq) > 0     0.02      0.25    -0.37     0.43       1.19      0.54     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Same for iconic gestures:

iconic_freq_mdl <- brm(iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type + log_freq +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = df,
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(iconic_freq_mdl, file = '../models/iconic_freq_mdl.RData')

Load:

load('../models/iconic_freq_mdl.RData')

Show model:

iconic_freq_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: iconic_gesture ~ 1 + type + log_freq + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1547) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 838) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.20      0.33     1.61     2.89 1.00     1953     4075
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.71      0.34     1.16     2.47 1.00     2846     4565
## 
## Regression Coefficients:
##            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept     -4.75      1.08    -7.02    -2.77 1.00     3965     5184
## typeiconic     1.83      0.74     0.44     3.31 1.00     4050     5288
## log_freq       0.32      0.32    -0.31     0.98 1.00     4040     4644
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check effects:

hypothesis(iconic_freq_mdl, 'typeiconic > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (typeiconic) > 0     1.83      0.74     0.66     3.08     180.82      0.99
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_freq_mdl, 'log_freq > 0')

## Hypothesis Tests for class b:
##       Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (log_freq) > 0     0.32      0.32    -0.21     0.86        5.4      0.84     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Next look at other:

other_freq_mdl <- brm(non_iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type + log_freq +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = filter(df, !is.na(non_iconic_gesture)),
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(other_freq_mdl, file = '../models/other_freq_mdl.RData')

Load:

load('../models/other_freq_mdl.RData')

Show model:

other_freq_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: non_iconic_gesture ~ 1 + type + log_freq + (1 | word) + (1 | url) 
##    Data: filter(df, !is.na(non_iconic_gesture)) (Number of observations: 1334) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 734) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.36      0.29     1.85     2.98 1.00     1589     3558
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.24      0.25     0.81     1.80 1.00     2582     4578
## 
## Regression Coefficients:
##            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept     -0.41      0.76    -1.91     1.07 1.00     4461     4812
## typeiconic    -0.40      0.56    -1.52     0.67 1.00     4717     4988
## log_freq       0.06      0.25    -0.44     0.53 1.00     3968     4450
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check effects:

hypothesis(other_freq_mdl, 'typeiconic < 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (typeiconic) < 0     -0.4      0.56    -1.34      0.5       3.28      0.77
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_freq_mdl, 'log_freq > 0')

## Hypothesis Tests for class b:
##       Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (log_freq) > 0     0.06      0.25    -0.35     0.45       1.47      0.59     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

7.4 Posterior distributions

Show the posterior:

gesture_mdl_posts <- posterior_samples(gesture_freq_mdl)

## Warning: Method 'posterior_samples' is deprecated. Please see ?as_draws for
## recommended alternatives.

Make a plot of the posterior distribution of the type coefficient:

# Plot basics:

gesture_posts_p <- gesture_mdl_posts |> 
  ggplot(aes(x = b_typeiconic)) +
  geom_density(fill = 'purple3') +
  geom_vline(xintercept = 0, linetype = 'dashed')

# Axes and labels:

gesture_posts_p <- gesture_posts_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.2),
                     breaks = seq(0, 1.2, 0.2)) +
  scale_x_continuous(limits = c(-3.5, 3.5),
                     breaks = seq(-3, 3, 1))

# Look and feel:

gesture_posts_p <- gesture_posts_p +
  ylab('Density') +
  xlab('Posterior estimate') +
  theme_classic()

# Show and save:

gesture_posts_p

ggsave(plot = gesture_posts_p, filename = '../figures/gesture_posterior_with_freq.pdf',
       width = 4.7, height = 3)

Show the posterior of the type coefficient. First, extract the posterior samples:

iconic_mdl_posts <- posterior_samples(iconic_freq_mdl)

## Warning: Method 'posterior_samples' is deprecated. Please see ?as_draws for
## recommended alternatives.

Make a plot of the posterior distribution of the coefficient:

# Plot basics:

iconic_posts_p <- iconic_mdl_posts |> 
  ggplot(aes(x = b_typeiconic)) +
  geom_density(fill = 'purple3') +
  geom_vline(xintercept = 0, linetype = 'dashed')

# Axes and labels:

iconic_posts_p <- iconic_posts_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.2),
                     breaks = seq(0, 1.2, 0.2)) +
  scale_x_continuous(limits = c(-3.5, 3.5),
                     breaks = seq(-3, 3, 1))

# Look and feel:

iconic_posts_p <- iconic_posts_p +
  ylab('Density of posterior samples') +
  xlab('Posterior estimate') +
  theme_classic()

# Show and save:

iconic_posts_p

## Warning: Removed 121 rows containing non-finite outside the scale range
## (`stat_density()`).

ggsave(plot = iconic_posts_p, filename = '../figures/iconic_gesture_posterior_with_freq.pdf',
       width = 4.7, height = 3)

## Warning: Removed 121 rows containing non-finite outside the scale range
## (`stat_density()`).

Show the posterior of the type coefficient. First, extract the posterior samples:

other_mdl_posts <- posterior_samples(other_freq_mdl)

## Warning: Method 'posterior_samples' is deprecated. Please see ?as_draws for
## recommended alternatives.

Make a plot of the posterior distribution of the coefficient:

# Plot basics:

other_posts_p <- other_mdl_posts |> 
  ggplot(aes(x = b_typeiconic)) +
  geom_density(fill = 'purple3') +
  geom_vline(xintercept = 0, linetype = 'dashed')

# Axes and labels:

other_posts_p <- other_posts_p +
  scale_y_continuous(expand = c(0, 0),
                     limits = c(0, 1.2),
                     breaks = seq(0, 1.2, 0.2)) +
  scale_x_continuous(limits = c(-3.5, 3.5),
                     breaks = seq(-3, 3, 1))

# Look and feel:

other_posts_p <- other_posts_p +
  ylab('Density of posterior samples') +
  xlab('Posterior estimate') +
  theme_classic()

# Show and save:

other_posts_p

ggsave(plot = other_posts_p, filename = '../figures/other_gesture_posterior_with_freq.pdf',
       width = 4.7, height = 3)

Put them all together into one plot:

gesture_posts_p <- gesture_posts_p +
  ggtitle('a) Any gestures') +
  theme(plot.title = element_text(face = 'bold', size = 12))

iconic_posts_p <- iconic_posts_p + ylab(NULL) +
  ggtitle('b) Iconic gestures') +
  theme(plot.title = element_text(face = 'bold', size = 12))

other_posts_p <- other_posts_p + ylab(NULL) +
  ggtitle('c) Non-iconic gestures') +
  theme(plot.title = element_text(face = 'bold', size = 12))

three_p <- gesture_posts_p + plot_spacer() + iconic_posts_p + plot_spacer() + other_posts_p +
  plot_layout(widths = c(4, 0.1, 4, 0.1, 4))

ggsave(plot = three_p,
       filename = '../figures/all_posteriors_with_frequency.pdf',
       width = 9.5, height = 2.5)

## Warning: Removed 121 rows containing non-finite outside the scale range
## (`stat_density()`).

8 POS effect

First, count how many unique adjectives and verbs there are:

distinct(df, word, POS) |> 
  count(POS)

## # A tibble: 2 × 2
##   POS           n
##   <chr>     <int>
## 1 adjective    15
## 2 verb         30

Check the average proportion of all gestures, separately for high/low iconicity and POS:

df |> 
  count(POS, type, gesture) |> 
  group_by(POS, type) |> 
  mutate(proportion = n / sum(n),
         percentage = str_c(round(proportion, 3) * 100, '%'))

## # A tibble: 8 × 6
## # Groups:   POS, type [4]
##   POS       type       gesture     n proportion percentage
##   <chr>     <fct>        <dbl> <int>      <dbl> <chr>     
## 1 adjective non_iconic       0    91      0.464 46.4%     
## 2 adjective non_iconic       1   105      0.536 53.6%     
## 3 adjective iconic           0    77      0.407 40.7%     
## 4 adjective iconic           1   112      0.593 59.3%     
## 5 verb      non_iconic       0   423      0.495 49.5%     
## 6 verb      non_iconic       1   432      0.505 50.5%     
## 7 verb      iconic           0    73      0.239 23.9%     
## 8 verb      iconic           1   233      0.761 76.1%

Next, iconic gestures:

df |> 
  count(POS, type, iconic_gesture) |> 
  filter(!is.na(iconic_gesture)) |> 
  group_by(POS, type) |> 
  mutate(proportion = n / sum(n),
         percentage = str_c(round(proportion, 3) * 100, '%'))

## # A tibble: 8 × 6
## # Groups:   POS, type [4]
##   POS       type       iconic_gesture     n proportion percentage
##   <chr>     <fct>               <dbl> <int>      <dbl> <chr>     
## 1 adjective non_iconic              0   171     0.872  87.2%     
## 2 adjective non_iconic              1    25     0.128  12.8%     
## 3 adjective iconic                  0   173     0.915  91.5%     
## 4 adjective iconic                  1    16     0.0847 8.5%      
## 5 verb      non_iconic              0   778     0.911  91.1%     
## 6 verb      non_iconic              1    76     0.0890 8.9%      
## 7 verb      iconic                  0   213     0.696  69.6%     
## 8 verb      iconic                  1    93     0.304  30.4%

Next, all other gestures:

df |> 
  count(POS, type, non_iconic_gesture) |> 
  filter(!is.na(non_iconic_gesture)) |> 
  group_by(POS, type) |> 
  mutate(proportion = n / sum(n),
         percentage = str_c(round(proportion, 3) * 100, '%'))

## # A tibble: 8 × 6
## # Groups:   POS, type [4]
##   POS       type       non_iconic_gesture       n proportion percentage
##   <chr>     <fct>      <chr>                <int>      <dbl> <chr>     
## 1 adjective non_iconic gesture (non-iconic)    80      0.468 46.8%     
## 2 adjective non_iconic no gesture              91      0.532 53.2%     
## 3 adjective iconic     gesture (non-iconic)    96      0.555 55.5%     
## 4 adjective iconic     no gesture              77      0.445 44.5%     
## 5 verb      non_iconic gesture (non-iconic)   355      0.456 45.6%     
## 6 verb      non_iconic no gesture             423      0.544 54.4%     
## 7 verb      iconic     gesture (non-iconic)   140      0.657 65.7%     
## 8 verb      iconic     no gesture              73      0.343 34.3%

Let’s fit a model with a fixed effect of type, and now added to this the POS effect, and random intercepts for word and url because we have multiple data points for each of these grouping factors. We cannot fit type random slopes here because there is no possible variation whatsoever of type within word or url since each word or video is always either iconic or not iconic.

This time around, it makes sense to sum-code POS and type (dummy codes of -1, +1) so that we can interpret main effects in the presence of interactions more easily.

# Make into factor:

df <- mutate(df,
             type_c = factor(type, levels = c('iconic \nword', 'non-iconic \nword')),
             POS_c = factor(POS, levels = c('verb', 'adjective')))

# Add sum-coding contrast coding scheme for 2 categories:

contrasts(df$type_c) <- contr.sum(2)
contrasts(df$POS_c) <- contr.sum(2)

# Check:

contrasts(df$type_c)

##                   [,1]
## iconic \nword        1
## non-iconic \nword   -1

contrasts(df$POS_c)

##           [,1]
## verb         1
## adjective   -1

Now, fit the model:

gesture_POS_mdl <- brm(gesture ~
                     
                     # Fixed effects:
                     
                     1 + type_c + POS_c + type_c:POS_c +
                     
                     # Random effects:
                     
                     (1|word) + (1|url),
                   
                   # More model specs:
                   
                   prior = weak_priors,
                   family = bernoulli,
                   data = df,
                   
                   # MCMC estimation specs:
                   
                   seed = 42, cores = 4,
                   iter = 4000, warmup = 2000)

# Save:

save(gesture_POS_mdl, file = '../models/gesture_POS_mdl.RData')

Load and show model:

# Load:

load('../models/gesture_POS_mdl.Rdata')

# Show:

gesture_POS_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: gesture ~ 1 + type_c + POS_c + type_c:POS_c + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1546) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.26      0.26     1.80     2.83 1.00     1811     3312
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.29      0.24     0.88     1.82 1.00     3258     4783
## 
## Regression Coefficients:
##                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept          0.90      0.28     0.36     1.46 1.00     5624     5338
## type_c1            0.43      0.27    -0.09     0.98 1.00     5918     5876
## POS_c1             0.44      0.27    -0.08     0.99 1.00     5154     5066
## type_c1:POS_c1     0.26      0.26    -0.26     0.77 1.00     5543     5689
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

This is to calculate the actual posterior probability of the effect being positive (= of the same sign), which is essentially just pinning a number to what proportion of the area in the distribution above is to the right of the dashed line.

hypothesis(gesture_POS_mdl, 'type_c1 > 0')

## Hypothesis Tests for class b:
##      Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (type_c1) > 0     0.43      0.27    -0.01     0.88      17.06      0.94     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_POS_mdl, 'POS_c1 > 0')

## Hypothesis Tests for class b:
##     Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (POS_c1) > 0     0.44      0.27     0.01     0.89      21.22      0.96    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_POS_mdl, 'type_c1:POS_c1 > 0')

## Hypothesis Tests for class b:
##             Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (type_c1:POS_c1) > 0     0.26      0.26    -0.16     0.69       5.41
##   Post.Prob Star
## 1      0.84     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Same for iconic gestures:

iconic_POS_mdl <- brm(iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type_c + POS_c + type_c:POS_c +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = df,
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(iconic_POS_mdl, file = '../models/iconic_POS_mdl.RData')

Load and show model:

# Load model:

load('../models/iconic_POS_mdl.RData')

# Show model:

iconic_POS_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: iconic_gesture ~ 1 + type_c + POS_c + type_c:POS_c + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1545) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.28      0.34     1.68     3.02 1.00     1752     3520
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.53      0.33     0.98     2.27 1.00     2506     3803
## 
## Regression Coefficients:
##                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept         -3.43      0.45    -4.41    -2.62 1.00     2759     3988
## type_c1            0.62      0.34    -0.03     1.32 1.00     4360     5106
## POS_c1             0.62      0.34    -0.01     1.30 1.00     4793     5407
## type_c1:POS_c1     0.57      0.34    -0.09     1.25 1.00     4801     5244
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(iconic_POS_mdl, 'type_c1 > 0')

## Hypothesis Tests for class b:
##      Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (type_c1) > 0     0.62      0.34     0.07     1.18      31.39      0.97    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_POS_mdl, 'POS_c1 > 0')

## Hypothesis Tests for class b:
##     Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (POS_c1) > 0     0.62      0.34     0.08     1.17       35.2      0.97    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_POS_mdl, 'type_c1:POS_c1 > 0')

## Hypothesis Tests for class b:
##             Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (type_c1:POS_c1) > 0     0.57      0.34     0.02     1.14      21.66
##   Post.Prob Star
## 1      0.96    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

The final model is the one with only the non-iconic gestures:

Same for non-iconic (= “other”) gestures:

other_POS_mdl <- brm(non_iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type_c + POS_c + type_c:POS_c +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = filter(df, !is.na(non_iconic_gesture)),
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(other_POS_mdl, file = '../models/other_POS_mdl.RData')

Load and show model:

# Load model:

load('../models/other_POS_mdl.RData')

# Show model:

other_POS_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: non_iconic_gesture ~ 1 + type_c + POS_c + type_c:POS_c + (1 | word) + (1 | url) 
##    Data: filter(df, !is.na(non_iconic_gesture)) (Number of observations: 1335) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 736) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.37      0.29     1.85     3.00 1.00     1555     3449
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.26      0.25     0.82     1.81 1.00     2942     5285
## 
## Regression Coefficients:
##                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept         -0.42      0.27    -0.96     0.14 1.00     6211     5528
## type_c1           -0.24      0.27    -0.78     0.29 1.00     5142     4873
## POS_c1            -0.26      0.27    -0.82     0.29 1.00     5765     5222
## type_c1:POS_c1    -0.12      0.27    -0.64     0.40 1.00     5172     5333
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(other_POS_mdl, 'type_c1 < 0')

## Hypothesis Tests for class b:
##      Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (type_c1) < 0    -0.24      0.27    -0.68     0.19       4.51      0.82     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_POS_mdl, 'POS_c1 < 0')

## Hypothesis Tests for class b:
##     Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
## 1 (POS_c1) < 0    -0.26      0.27    -0.72     0.19       5.28      0.84     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_POS_mdl, 'type_c1:POS_c1 < 0')

## Hypothesis Tests for class b:
##             Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (type_c1:POS_c1) < 0    -0.12      0.27    -0.55     0.31       2.05
##   Post.Prob Star
## 1      0.67     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

9 Incorporating modality differences

9.1 Merge data into main data

Load Lancaster data:

lanc <- read_csv('../data/Lancaster_sensorimotor_norms_for_39707_words.csv')

# Show:

lanc

## # A tibble: 39,707 × 45
##    Word        Auditory.mean Gustatory.mean Haptic.mean Interoceptive.mean
##    <chr>               <dbl>          <dbl>       <dbl>              <dbl>
##  1 A                   2.21          0           0.429              0     
##  2 A CAPPELLA          4.33          0           0.222              0.722 
##  3 AARDVARK            1.62          0.562       1.62               0.0625
##  4 ABACK               1.29          0.0588      0.294              1.35  
##  5 ABACUS              1.56          0.167       3.72               0.278 
##  6 ABANDON             0.941         0.118       0.294              2.12  
##  7 ABANDONED           1.44          0           0.0556             1.67  
##  8 ABANDONEE           1.94          0           1.38               0.562 
##  9 ABANDONER           0.571         0           0.143              1.64  
## 10 ABANDONMENT         2.13          0.0667      1.2                2.93  
## # ℹ 39,697 more rows
## # ℹ 40 more variables: Olfactory.mean <dbl>, Visual.mean <dbl>,
## #   Foot_leg.mean <dbl>, Hand_arm.mean <dbl>, Head.mean <dbl>,
## #   Mouth.mean <dbl>, Torso.mean <dbl>, Auditory.SD <dbl>, Gustatory.SD <dbl>,
## #   Haptic.SD <dbl>, Interoceptive.SD <dbl>, Olfactory.SD <dbl>,
## #   Visual.SD <dbl>, Foot_leg.SD <dbl>, Hand_arm.SD <dbl>, Head.SD <dbl>,
## #   Mouth.SD <dbl>, Torso.SD <dbl>, Max_strength.perceptual <dbl>, …

There are only dominant auditory, gustatory, haptic, and visual words for the iconic words, so we’ll extract the perceptual strength measures only for that and for olfaction to complete the five senses.

Make Word lowercase, both in the column name and in the actual content of the column:

lanc <- lanc |> 
  rename(word = Word,
         dominant_modality = Dominant.perceptual,
         dominant_action = Dominant.action,
         auditory_strength = Auditory.mean,
         visual_strength = Visual.mean,
         haptic_strength = Haptic.mean,
         gustatory_strength = Gustatory.mean,
         olfactory_strength = Olfactory.mean,
         hand_arm_mean = Hand_arm.mean,
         max_strength = Max_strength.perceptual,
         head_mean = Head.mean,
         foot_leg_mean = Foot_leg.mean,
         mouth_mean = Mouth.mean,
         torso_mean = Torso.mean,
         max_action = Max_strength.action) |> 
  mutate(word = str_to_lower(word))

Merge with main data:

df <- left_join(df,
                select(lanc, word, dominant_modality, dominant_action,
                       auditory_strength, visual_strength, haptic_strength,
                       gustatory_strength, olfactory_strength,
                       hand_arm_mean, foot_leg_mean, mouth_mean, torso_mean, head_mean,
                       max_strength, max_action))

## Joining with `by = join_by(word)`

Merge with proportion table:

by_word_all <- left_join(by_word_all,
                         select(lanc, word, dominant_modality, dominant_action,
                                auditory_strength, visual_strength, haptic_strength,
                                gustatory_strength, olfactory_strength,
                                max_strength, max_action))

## Joining with `by = join_by(word)`

# Save outside of R:

by_word_all |> 
  write_csv('../data/by_word_proportions_with_modality.csv')

Which words are classified how?

select(by_word_all,
       word, type, dominant_modality, dominant_action) |> 
  print(n = Inf)

## # A tibble: 45 × 4
##    word      type            dominant_modality dominant_action
##    <chr>     <fct>           <chr>             <chr>          
##  1 said      non-iconic word Auditory          Mouth          
##  2 spank     iconic word     Haptic            Hand_arm       
##  3 slushy    iconic word     Visual            Mouth          
##  4 realize   non-iconic word Interoceptive     Head           
##  5 inform    non-iconic word Auditory          Mouth          
##  6 wearing   non-iconic word Visual            Foot_leg       
##  7 yucky     iconic word     Gustatory         Mouth          
##  8 knew      non-iconic word Interoceptive     Head           
##  9 filling   non-iconic word Visual            Mouth          
## 10 other     non-iconic word Visual            Head           
## 11 exact     non-iconic word Visual            Head           
## 12 grateful  non-iconic word Interoceptive     Head           
## 13 prevail   non-iconic word Interoceptive     Head           
## 14 squish    iconic word     Haptic            Hand_arm       
## 15 tamper    non-iconic word Visual            Hand_arm       
## 16 splotch   iconic word     Visual            Head           
## 17 put       non-iconic word Visual            Hand_arm       
## 18 confirmed non-iconic word Visual            Mouth          
## 19 rejoin    non-iconic word Visual            Head           
## 20 discern   non-iconic word Visual            Head           
## 21 jealous   non-iconic word Interoceptive     Head           
## 22 puffy     iconic word     Visual            Head           
## 23 covet     non-iconic word Interoceptive     Head           
## 24 ordain    non-iconic word Visual            Mouth          
## 25 swish     iconic word     Visual            Head           
## 26 wring     iconic word     Haptic            Hand_arm       
## 27 saggy     iconic word     Visual            Head           
## 28 swoosh    iconic word     Auditory          Hand_arm       
## 29 zap       iconic word     Haptic            Hand_arm       
## 30 outwit    non-iconic word Visual            Head           
## 31 chomp     iconic word     Visual            Mouth          
## 32 crispy    iconic word     Haptic            Mouth          
## 33 absent    non-iconic word Visual            Head           
## 34 wheeze    iconic word     Auditory          Mouth          
## 35 woof      iconic word     Auditory          Head           
## 36 sullen    non-iconic word Visual            Head           
## 37 barking   iconic word     Auditory          Head           
## 38 acquaint  non-iconic word Visual            Head           
## 39 bang      iconic word     Auditory          Head           
## 40 munch     iconic word     Gustatory         Mouth          
## 41 plump     iconic word     Visual            Head           
## 42 wobbly    iconic word     Visual            Foot_leg       
## 43 barren    non-iconic word Visual            Head           
## 44 snap      iconic word     Auditory          Hand_arm       
## 45 gooey     iconic word     Haptic            Hand_arm

9.2 Descriptive statistics & data visualization

Descriptive averages by dominant modality, also with counts:

# Create count table:

modality_type_counts <- by_word_all |>
  count(type, dominant_modality)

# Create descriptive averages and merge with counts:

by_word_all |> 
  group_by(type, dominant_modality) |> 
  summarize(M_gesture = mean(gesture_proportion),
            M_iconic = mean(iconic_gesture_proportion),
            M_other = mean(other_proportion)) |> 
  left_join(modality_type_counts)

## `summarise()` has grouped output by 'type'. You can override using the
## `.groups` argument.
## Joining with `by = join_by(type, dominant_modality)`

## # A tibble: 7 × 6
## # Groups:   type [2]
##   type            dominant_modality M_gesture M_iconic M_other     n
##   <fct>           <chr>                 <dbl>    <dbl>   <dbl> <int>
## 1 non-iconic word Auditory              0.262   0.0774   0.185     2
## 2 non-iconic word Interoceptive         0.488   0.0634   0.422     6
## 3 non-iconic word Visual                0.620   0.132    0.488    15
## 4 iconic word     Auditory              0.717   0.238    0.479     6
## 5 iconic word     Gustatory             0.532   0.118    0.414     2
## 6 iconic word     Haptic                0.662   0.311    0.352     6
## 7 iconic word     Visual                0.727   0.215    0.511     8

Clearly shows that visual words have the highest gesture rate, regardless of whether they are iconic or not, and for iconic words, haptic, visual, and auditory words have higher gesture rates than gustatory ones, although there’s only two of those, so we have to be careful not to over-interpret this as it very much hinges on these specific iconic words chosen. This data sparsity issue is only a concern with the categorical modality labels however, as of course the continuous ratings exist for all words.

Descriptive averages by dominant action:

# Create count table:

action_type_counts <- by_word_all |>
  count(type, dominant_action)

# Create descriptive averages and merge with counts:

by_word_all |> 
  group_by(type, dominant_action) |> 
  summarize(M_gesture = mean(gesture_proportion),
            M_iconic = mean(iconic_gesture_proportion),
            M_other = mean(other_proportion)) |> 
  left_join(action_type_counts)

## `summarise()` has grouped output by 'type'. You can override using the
## `.groups` argument.
## Joining with `by = join_by(type, dominant_action)`

## # A tibble: 8 × 6
## # Groups:   type [2]
##   type            dominant_action M_gesture M_iconic M_other     n
##   <fct>           <chr>               <dbl>    <dbl>   <dbl> <int>
## 1 non-iconic word Foot_leg            0.714   0.0536   0.661     1
## 2 non-iconic word Hand_arm            0.705   0.325    0.380     2
## 3 non-iconic word Head                0.539   0.0973   0.441    15
## 4 non-iconic word Mouth               0.508   0.0702   0.438     5
## 5 iconic word     Foot_leg            0.8     0.6      0.2       1
## 6 iconic word     Hand_arm            0.704   0.275    0.429     7
## 7 iconic word     Head                0.701   0.233    0.468     8
## 8 iconic word     Mouth               0.637   0.143    0.494     6

There’s only two foot/leg words, so we shouldn’t really interpret that. For iconic words, the action ratings don’t seem to matter as much as the modality, with Mouth a bit lower.

Plot proportions as a function of auditory_strength and the other perceptual measures. We’ll use a facet wrap for this and so for that, it would make sense to have all the strength measures in long format, with an indicator variable saying what strength it is:

by_word_long <- by_word_all |> 
  select(type, word, gesture_proportion, iconic_gesture_proportion, other_proportion,
         auditory_strength:olfactory_strength) |> 
  pivot_longer(cols = auditory_strength:olfactory_strength,
               names_to = 'modality',
               values_to = 'strength')

# Show a few random rows:

by_word_long |> 
  sample_n(10)

## # A tibble: 10 × 7
##    type         word  gesture_proportion iconic_gesture_propo…¹ other_proportion
##    <fct>        <chr>              <dbl>                  <dbl>            <dbl>
##  1 non-iconic … info…              0.158                 0.105            0.0526
##  2 iconic word  slus…              0.731                 0.119            0.612 
##  3 iconic word  cris…              0.714                 0.0714           0.643 
##  4 iconic word  spank              0.691                 0.124            0.567 
##  5 non-iconic … conf…              0.471                 0.0588           0.412 
##  6 non-iconic … rejo…              0.5                   0.0588           0.441 
##  7 non-iconic … info…              0.158                 0.105            0.0526
##  8 non-iconic … wear…              0.714                 0.0536           0.661 
##  9 non-iconic … tamp…              0.639                 0.222            0.417 
## 10 non-iconic … exact              0.826                 0.217            0.609 
## # ℹ abbreviated name: ¹​iconic_gesture_proportion
## # ℹ 2 more variables: modality <chr>, strength <dbl>

Make a plot out of this, for overall gesture proportion:

# Plot basics:

modality_p <- by_word_long |> 
  ggplot(aes(x = strength, y = gesture_proportion, col = type)) +
  geom_smooth(method = 'lm') +
  geom_point()

# Axis and labels:

modality_p <- modality_p +
  ylab('Gesture proportion') +
  xlab('Perceptual strength rating') +
  scale_color_manual(values = c('steelblue', 'goldenrod3')) +
  facet_wrap(~modality)

# Look and feel:

modality_p <- modality_p +
  theme_classic() +
  theme(legend.position = 'bottom')

# Show and save:

modality_p

## `geom_smooth()` using formula = 'y ~ x'

ggsave(plot = modality_p,
       filename = '../figures/modality_scatterplot_matrix.pdf',
       width = 12, height = 6)

## `geom_smooth()` using formula = 'y ~ x'

Same for iconic gesture proportion:

# Plot basics:

modality_iconicity_p <- by_word_long |> 
  ggplot(aes(x = strength, y = iconic_gesture_proportion,
             col = type)) +
  geom_smooth(method = 'lm') +
  geom_point() +
  facet_wrap(~modality)

# Axis and labels:

modality_iconicity_p <- modality_iconicity_p +
  ylab('Gesture proportion') +
  xlab('Perceptual strength rating') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'))

# Look and feel:

modality_iconicity_p <- modality_iconicity_p +
  theme_classic() +
  theme(legend.position = 'bottom')

# Show and save:

modality_iconicity_p

## `geom_smooth()` using formula = 'y ~ x'

ggsave(plot = modality_iconicity_p,
       filename = '../figures/modality_scatterplot_matrix_iconic_gestures.pdf',
       width = 12, height = 6)

## `geom_smooth()` using formula = 'y ~ x'

Do the same but a single scatterplot with just the max strength, and then the max action.

Make a plot out of this, for overall gesture proportion:

# Plot basics:

modality_p <- by_word_all |> 
  ggplot(aes(x = max_strength, y = gesture_proportion,
             col = type, label = word)) +
  geom_smooth(method = 'lm') +
  geom_text()

# Axis and labels:

modality_p <- modality_p +
  ylab('Gesture proportion') +
  xlab('Max perceptual strength rating') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'))

# Look and feel:

modality_p <- modality_p +
  theme_classic() +
  theme(legend.position = 'bottom')

# Show and save:

modality_p

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

ggsave(plot = modality_p,
       filename = '../figures/max_strength_scatterplot.pdf',
       width = 6.5, height = 4.5)

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

Not necessarily what one would expect, but pretty much anything is compatible with this data since the confidence regions are so wide.

Same for iconic gesture proportion:

# Plot basics:

modality_p <- by_word_all |> 
  ggplot(aes(x = max_strength, y = iconic_gesture_proportion,
             col = type, label = word)) +
  geom_smooth(method = 'lm') +
  geom_text()

# Axis and labels:

modality_p <- modality_p +
  ylab('Iconic gesture proportion') +
  xlab('Max perceptual strength rating') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'))

# Look and feel:

modality_p <- modality_p +
  theme_classic() +
  theme(legend.position = 'bottom')

# Show and save:

modality_p

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

ggsave(plot = modality_p,
       filename = '../figures/max_strength_scatterplot_iconic_gestures.pdf',
       width = 6.5, height = 4.5)

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

This looks like it’s more the specific affordances of the verb semantics in terms of iconicity than anything in relation to how much sensory content there is overall.

Same with action strength:

Make a plot out of this, for overall gesture proportion:

# Plot basics:

action_p <- by_word_all |> 
  ggplot(aes(x = max_action, y = gesture_proportion,
             col = type, label = word)) +
  geom_smooth(method = 'lm') +
  geom_text()

# Axis and labels:

action_p <- action_p +
  ylab('Gesture proportion') +
  xlab('Max motor strength rating') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'))

# Look and feel:

action_p <- action_p +
  theme_classic() +
  theme(legend.position = 'bottom')

# Show and save:

action_p

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

ggsave(plot = action_p,
       filename = '../figures/max_action_scatterplot.pdf',
       width = 6.5, height = 4.5)

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

Nothing much going on.

Same for iconic gesture proportion:

# Plot basics:

action_p <- by_word_all |> 
  ggplot(aes(x = max_action, y = iconic_gesture_proportion,
             col = type, label = word)) +
  geom_smooth(method = 'lm') +
  geom_text()

# Axis and labels:

action_p <- action_p +
  ylab('Iconic gesture proportion') +
  xlab('Max action strength rating') +
  scale_color_manual(values = c('steelblue', 'goldenrod3'))

# Look and feel:

action_p <- action_p +
  theme_classic() +
  theme(legend.position = 'bottom')

# Show and save:

action_p

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

ggsave(plot = action_p,
       filename = '../figures/max_action_scatterplot_iconic_gestures.pdf',
       width = 6.5, height = 4.5)

## `geom_smooth()` using formula = 'y ~ x'

## Warning: The following aesthetics were dropped during statistical transformation: label.
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

9.3 Build models: max sensorimotor strength ones

Model with max perceptual strength, action strength, and iconicity:

gesture_mod_mdl <- brm(gesture ~
                     
                     # Fixed effects:
                     
                     1 + type + max_strength + max_action + 
                     
                     # Random effects:
                     
                     (1|word) + (1|url),
                   
                   # More model specs:
                   
                   prior = weak_priors,
                   family = bernoulli,
                   data = df,
                   
                   # MCMC estimation specs:
                   
                   seed = 42, cores = 4,
                   iter = 4000, warmup = 2000)

# Save:

save(gesture_mod_mdl, file = '../models/gesture_mod_mdl.RData')

Load and show model:

# Load:

load('../models/gesture_mod_mdl.Rdata')

# Show:

gesture_mod_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: gesture ~ 1 + type + max_strength + max_action + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1546) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.26      0.26     1.78     2.79 1.00     1686     3417
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.33      0.24     0.91     1.87 1.00     2448     4103
## 
## Regression Coefficients:
##              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        1.96      1.43    -0.87     4.73 1.00     3891     5149
## typeiconic       1.14      0.53     0.12     2.20 1.00     3544     4831
## max_strength    -0.46      0.42    -1.27     0.36 1.00     3638     4732
## max_action       0.02      0.28    -0.52     0.57 1.00     3346     4488
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

This is to calculate the actual posterior probability of the effect being positive (= of the same sign), which is essentially just pinning a number to what proportion of the area in the distribution above is to the right of the dashed line.

hypothesis(gesture_mod_mdl, 'typeiconic > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (typeiconic) > 0     1.14      0.53     0.29     2.02      61.99      0.98
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_mod_mdl, 'max_strength < 0')

## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (max_strength) < 0    -0.46      0.42    -1.13     0.23       6.55      0.87
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_mod_mdl, 'max_action > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (max_action) > 0     0.02      0.28    -0.43     0.47       1.11      0.53
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Same for iconic gestures:

iconic_mod_mdl <- brm(iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type + max_strength + max_action + 
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = df,
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(iconic_mod_mdl, file = '../models/iconic_mod_mdl.RData')

Load and show model:

# Load model:

load('../models/iconic_mod_mdl.RData')

# Show model:

iconic_mod_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: iconic_gesture ~ 1 + type + max_strength + max_action + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1545) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.27      0.34     1.68     3.00 1.00     2107     3766
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.77      0.35     1.18     2.56 1.00     2873     4740
## 
## Regression Coefficients:
##              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept       -4.59      2.02    -8.77    -0.82 1.00     4621     4959
## typeiconic       1.50      0.71     0.15     2.91 1.00     3911     4671
## max_strength     0.10      0.55    -0.99     1.22 1.00     4480     5095
## max_action       0.08      0.36    -0.61     0.79 1.00     4063     4742
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(iconic_mod_mdl, 'typeiconic > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (typeiconic) > 0      1.5      0.71     0.37     2.67      62.49      0.98
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_mod_mdl, 'max_strength > 0')

## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (max_strength) > 0      0.1      0.55    -0.79     1.03       1.31      0.57
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_mod_mdl, 'max_action > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (max_action) > 0     0.08      0.36     -0.5     0.67       1.42      0.59
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

The final model is the one with only the non-iconic gestures:

Same for non-iconic (= “other”) gestures:

other_mod_mdl <- brm(non_iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + type + max_strength + max_action + 
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = filter(df, !is.na(non_iconic_gesture)),
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(other_mod_mdl, file = '../models/other_mod_mdl.RData')

Load and show model:

# Load model:

load('../models/other_mod_mdl.RData')

# Show model:

other_mod_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: non_iconic_gesture ~ 1 + type + max_strength + max_action + (1 | word) + (1 | url) 
##    Data: filter(df, !is.na(non_iconic_gesture)) (Number of observations: 1335) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 736) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.35      0.29     1.80     2.95 1.00     1567     3191
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.22      0.25     0.79     1.76 1.00     2583     4036
## 
## Regression Coefficients:
##              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept       -1.84      1.36    -4.56     0.79 1.00     3763     4548
## typeiconic      -0.71      0.53    -1.78     0.30 1.00     3340     4398
## max_strength     0.49      0.41    -0.29     1.29 1.00     3432     4423
## max_action       0.01      0.27    -0.52     0.56 1.00     2843     4101
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(other_mod_mdl, 'typeiconic < 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (typeiconic) < 0    -0.71      0.53     -1.6     0.15       10.7      0.91
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_mod_mdl, 'max_strength > 0')

## Hypothesis Tests for class b:
##           Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (max_strength) > 0     0.49      0.41    -0.18     1.16       7.91      0.89
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_mod_mdl, 'max_action > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (max_action) > 0     0.01      0.27    -0.43     0.46       1.08      0.52
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

9.4 Build models: all perceptual variables

Model with all other variables:

gesture_all_senses_mdl <- brm(gesture ~
                     
                     # Fixed effects:
                     
                     1 + auditory_strength +
                       visual_strength +
                       haptic_strength +
                       gustatory_strength +
                       olfactory_strength +
                     
                     # Random effects:
                     
                     (1|word) + (1|url),
                   
                   # More model specs:
                   
                   prior = weak_priors,
                   family = bernoulli,
                   data = df,
                   
                   # MCMC estimation specs:
                   
                   seed = 42, cores = 4,
                   iter = 4000, warmup = 2000)

# Save:

save(gesture_all_senses_mdl, file = '../models/gesture_all_senses_mdl.RData')

Load and show model:

# Load:

load('../models/gesture_all_senses_mdl.Rdata')

# Show:

gesture_all_senses_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: gesture ~ 1 + auditory_strength + visual_strength + haptic_strength + gustatory_strength + olfactory_strength + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1546) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.31      0.27     1.83     2.89 1.00     1318     2752
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.25      0.26     0.82     1.82 1.00     2101     4090
## 
## Regression Coefficients:
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept             -1.25      1.22    -3.60     1.13 1.00     2383     3960
## auditory_strength      0.19      0.24    -0.27     0.67 1.00     2530     3881
## visual_strength        0.56      0.36    -0.15     1.26 1.00     2455     4097
## haptic_strength        0.34      0.26    -0.18     0.87 1.00     2765     3799
## gustatory_strength    -0.08      0.43    -0.95     0.77 1.00     2564     3537
## olfactory_strength    -0.22      0.68    -1.55     1.13 1.00     3341     4139
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

This is to calculate the actual posterior probability of the effect being positive (= of the same sign), which is essentially just pinning a number to what proportion of the area in the distribution above is to the right of the dashed line.

hypothesis(gesture_all_senses_mdl, 'auditory_strength > 0')

## Hypothesis Tests for class b:
##                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (auditory_strength) > 0     0.19      0.24    -0.19     0.59       3.59
##   Post.Prob Star
## 1      0.78     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_senses_mdl, 'visual_strength > 0')

## Hypothesis Tests for class b:
##              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (visual_strength) > 0     0.56      0.36    -0.03     1.14      16.02
##   Post.Prob Star
## 1      0.94     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_senses_mdl, 'haptic_strength > 0')

## Hypothesis Tests for class b:
##              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (haptic_strength) > 0     0.34      0.26    -0.08     0.77       9.77
##   Post.Prob Star
## 1      0.91     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_senses_mdl, 'gustatory_strength < 0')

## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (gustatory_strength) < 0    -0.08      0.43     -0.8     0.62       1.35
##   Post.Prob Star
## 1      0.57     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_senses_mdl, 'olfactory_strength < 0')

## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (olfactory_strength) < 0    -0.22      0.68    -1.33      0.9       1.75
##   Post.Prob Star
## 1      0.64     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Same for iconic gestures:

iconic_all_senses_mdl <- brm(iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + auditory_strength +
                       visual_strength +
                       haptic_strength +
                       gustatory_strength +
                       olfactory_strength +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = df,
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(iconic_all_senses_mdl, file = '../models/iconic_all_senses_mdl.RData')

Load and show model:

# Load model:

load('../models/iconic_all_senses_mdl.RData')

# Show model:

iconic_all_senses_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: iconic_gesture ~ 1 + auditory_strength + visual_strength + haptic_strength + gustatory_strength + olfactory_strength + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1545) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.35      0.35     1.71     3.10 1.00     1646     3235
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.72      0.36     1.11     2.54 1.00     2410     4322
## 
## Regression Coefficients:
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept             -5.72      1.75    -9.18    -2.33 1.00     2959     4408
## auditory_strength      0.55      0.32    -0.07     1.18 1.00     3319     4191
## visual_strength        0.08      0.49    -0.92     1.02 1.00     3088     4434
## haptic_strength        0.86      0.35     0.19     1.56 1.00     2817     4184
## gustatory_strength    -0.48      0.56    -1.64     0.58 1.00     3755     4239
## olfactory_strength     0.06      0.90    -1.70     1.87 1.00     4540     5507
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(iconic_all_senses_mdl, 'auditory_strength > 0')

## Hypothesis Tests for class b:
##                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (auditory_strength) > 0     0.55      0.32     0.02     1.08      21.86
##   Post.Prob Star
## 1      0.96    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_senses_mdl, 'visual_strength > 0')

## Hypothesis Tests for class b:
##              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (visual_strength) > 0     0.08      0.49    -0.74     0.86       1.33
##   Post.Prob Star
## 1      0.57     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_senses_mdl, 'haptic_strength > 0')

## Hypothesis Tests for class b:
##              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (haptic_strength) > 0     0.86      0.35     0.29     1.45     132.33
##   Post.Prob Star
## 1      0.99    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_senses_mdl, 'gustatory_strength < 0')

## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (gustatory_strength) < 0    -0.48      0.56    -1.43     0.42       4.33
##   Post.Prob Star
## 1      0.81     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_senses_mdl, 'olfactory_strength > 0')

## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (olfactory_strength) > 0     0.06       0.9    -1.41     1.55       1.11
##   Post.Prob Star
## 1      0.53     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

The final model is the one with only the non-iconic gestures:

Same for non-iconic (= “other”) gestures:

other_all_senses_mdl <- brm(non_iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + auditory_strength +
                       visual_strength +
                       haptic_strength +
                       gustatory_strength +
                       olfactory_strength +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = filter(df, !is.na(non_iconic_gesture)),
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(other_all_senses_mdl, file = '../models/other_all_senses_mdl.RData')

Load and show model:

# Load model:

load('../models/other_all_senses_mdl.RData')

# Show model:

other_all_senses_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: non_iconic_gesture ~ 1 + auditory_strength + visual_strength + haptic_strength + gustatory_strength + olfactory_strength + (1 | word) + (1 | url) 
##    Data: filter(df, !is.na(non_iconic_gesture)) (Number of observations: 1335) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 736) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.40      0.29     1.87     3.02 1.00     1808     3154
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.09      0.26     0.63     1.65 1.00     1750     2606
## 
## Regression Coefficients:
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept              1.18      1.14    -1.09     3.48 1.00     2829     4175
## auditory_strength      0.03      0.22    -0.42     0.47 1.00     3079     4285
## visual_strength       -0.65      0.35    -1.35     0.03 1.00     2700     3874
## haptic_strength       -0.01      0.25    -0.52     0.48 1.00     3209     4163
## gustatory_strength    -0.21      0.43    -1.04     0.66 1.00     3092     4328
## olfactory_strength     0.45      0.66    -0.85     1.76 1.00     3306     4590
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(other_all_senses_mdl, 'auditory_strength > 0')

## Hypothesis Tests for class b:
##                Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (auditory_strength) > 0     0.03      0.22    -0.34     0.39       1.24
##   Post.Prob Star
## 1      0.55     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_senses_mdl, 'visual_strength < 0')

## Hypothesis Tests for class b:
##              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (visual_strength) < 0    -0.65      0.35    -1.23     -0.1      33.48
##   Post.Prob Star
## 1      0.97    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_senses_mdl, 'haptic_strength < 0')

## Hypothesis Tests for class b:
##              Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (haptic_strength) < 0    -0.01      0.25    -0.43      0.4       1.05
##   Post.Prob Star
## 1      0.51     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_senses_mdl, 'gustatory_strength < 0')

## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (gustatory_strength) < 0    -0.21      0.43    -0.91     0.51       2.26
##   Post.Prob Star
## 1      0.69     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_senses_mdl, 'olfactory_strength > 0')

## Hypothesis Tests for class b:
##                 Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (olfactory_strength) > 0     0.45      0.66    -0.63     1.54       3.08
##   Post.Prob Star
## 1      0.76     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

9.5 Build models: all motor variables

Model with all other variables:

gesture_all_motor_mdl <- brm(gesture ~
                     
                     # Fixed effects:
                     
                     1 + hand_arm_mean +
                      head_mean +
                      foot_leg_mean +
                      mouth_mean +
                      torso_mean +
                     
                     # Random effects:
                     
                     (1|word) + (1|url),
                   
                   # More model specs:
                   
                   prior = weak_priors,
                   family = bernoulli,
                   data = df,
                   
                   # MCMC estimation specs:
                   
                   seed = 42, cores = 4,
                   iter = 4000, warmup = 2000)

# Save:

save(gesture_all_motor_mdl, file = '../models/gesture_all_motor_mdl.RData')

Load and show model:

# Load:

load('../models/gesture_all_motor_mdl.Rdata')

# Show:

gesture_all_motor_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: gesture ~ 1 + hand_arm_mean + head_mean + foot_leg_mean + mouth_mean + torso_mean + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1546) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.31      0.27     1.82     2.86 1.00     1661     3496
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.13      0.25     0.71     1.67 1.00     1947     3368
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept         1.89      1.18    -0.42     4.24 1.00     2397     3472
## hand_arm_mean     0.34      0.30    -0.24     0.97 1.00     2478     3786
## head_mean        -0.26      0.34    -0.94     0.42 1.00     2519     3709
## foot_leg_mean     0.54      0.44    -0.34     1.39 1.00     2657     4013
## mouth_mean       -0.35      0.21    -0.76     0.06 1.00     2536     3811
## torso_mean       -0.86      0.46    -1.77     0.04 1.00     2900     3744
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

This is to calculate the actual posterior probability of the effect being positive (= of the same sign), which is essentially just pinning a number to what proportion of the area in the distribution above is to the right of the dashed line.

hypothesis(gesture_all_motor_mdl, 'hand_arm_mean > 0')

## Hypothesis Tests for class b:
##            Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (hand_arm_mean) > 0     0.34       0.3    -0.15     0.85       6.84      0.87
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_motor_mdl, 'head_mean < 0')

## Hypothesis Tests for class b:
##        Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (head_mean) < 0    -0.26      0.34    -0.83      0.3       3.79      0.79
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_motor_mdl, 'foot_leg_mean > 0')

## Hypothesis Tests for class b:
##            Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (foot_leg_mean) > 0     0.54      0.44    -0.18     1.26       8.21      0.89
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_motor_mdl, 'torso_mean < 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (torso_mean) < 0    -0.86      0.46    -1.61    -0.12      31.39      0.97
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(gesture_all_motor_mdl, 'mouth_mean < 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (mouth_mean) < 0    -0.35      0.21    -0.69    -0.02      22.88      0.96
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

Same for iconic gestures:

iconic_all_motor_mdl <- brm(iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + hand_arm_mean +
                      head_mean +
                      foot_leg_mean +
                      mouth_mean +
                      torso_mean +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = df,
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(iconic_all_motor_mdl, file = '../models/iconic_all_motor_mdl.RData')

Load and show model:

# Load model:

load('../models/iconic_all_motor_mdl.RData')

# Show model:

iconic_all_motor_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: iconic_gesture ~ 1 + hand_arm_mean + head_mean + foot_leg_mean + mouth_mean + torso_mean + (1 | word) + (1 | url) 
##    Data: df (Number of observations: 1545) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 837) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.30      0.35     1.68     3.04 1.00     1600     3345
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     0.93      0.36     0.22     1.69 1.00     1011      902
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        -1.92      1.20    -4.34     0.51 1.00     3817     4488
## hand_arm_mean     0.57      0.31    -0.06     1.18 1.00     3198     4340
## head_mean        -0.55      0.36    -1.31     0.13 1.00     3965     4720
## foot_leg_mean     1.41      0.43     0.57     2.26 1.00     3629     4409
## mouth_mean       -0.32      0.21    -0.74     0.10 1.00     3815     4733
## torso_mean       -2.15      0.53    -3.23    -1.13 1.00     3179     4131
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(iconic_all_motor_mdl, 'hand_arm_mean > 0')

## Hypothesis Tests for class b:
##            Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (hand_arm_mean) > 0     0.57      0.31     0.05     1.06      25.85      0.96
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_motor_mdl, 'head_mean < 0')

## Hypothesis Tests for class b:
##        Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (head_mean) < 0    -0.55      0.36    -1.18     0.03       16.2      0.94
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_motor_mdl, 'foot_leg_mean > 0')

## Hypothesis Tests for class b:
##            Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (foot_leg_mean) > 0     1.41      0.43     0.71      2.1        799         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_motor_mdl, 'mouth_mean < 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (mouth_mean) < 0    -0.32      0.21    -0.66     0.02      16.09      0.94
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(iconic_all_motor_mdl, 'torso_mean < 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (torso_mean) < 0    -2.15      0.53    -3.03    -1.29        Inf         1
##   Star
## 1    *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

The final model is the one with only the non-iconic gestures:

Same for non-iconic (= “other”) gestures:

other_all_motor_mdl <- brm(non_iconic_gesture ~
                    
                    # Fixed effects:
                    
                    1 + hand_arm_mean +
                      head_mean +
                      foot_leg_mean +
                      mouth_mean +
                      torso_mean +
                    
                    # Random effects:
                    
                    (1|word) + (1|url),
                   
                  # More model specs:
                   
                  prior = weak_priors,
                  family = bernoulli,
                  data = filter(df, !is.na(non_iconic_gesture)),
                   
                  # MCMC estimation specs:
                  
                  seed = 42, cores = 4,
                  iter = 4000, warmup = 2000)

# Save:

save(other_all_motor_mdl, file = '../models/other_all_motor_mdl.RData')

Load and show model:

# Load model:

load('../models/other_all_motor_mdl.RData')

# Show model:

other_all_motor_mdl

##  Family: bernoulli 
##   Links: mu = logit 
## Formula: non_iconic_gesture ~ 1 + hand_arm_mean + head_mean + foot_leg_mean + mouth_mean + torso_mean + (1 | word) + (1 | url) 
##    Data: filter(df, !is.na(non_iconic_gesture)) (Number of observations: 1335) 
##   Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
##          total post-warmup draws = 8000
## 
## Multilevel Hyperparameters:
## ~url (Number of levels: 736) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     2.42      0.30     1.89     3.04 1.00     1490     3121
## 
## ~word (Number of levels: 45) 
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept)     1.20      0.27     0.74     1.78 1.00     2013     3150
## 
## Regression Coefficients:
##               Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept        -1.07      1.24    -3.54     1.36 1.00     2261     3505
## hand_arm_mean    -0.22      0.32    -0.87     0.41 1.00     2582     3706
## head_mean         0.09      0.36    -0.61     0.80 1.00     2417     3939
## foot_leg_mean     0.07      0.49    -0.89     1.04 1.00     2761     4059
## mouth_mean        0.32      0.22    -0.12     0.76 1.00     2108     2863
## torso_mean        0.18      0.50    -0.79     1.19 1.00     2870     3893
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

Check how many of them are of the same sign:

hypothesis(other_all_motor_mdl, 'hand_arm_mean < 0')

## Hypothesis Tests for class b:
##            Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (hand_arm_mean) < 0    -0.22      0.32    -0.75      0.3       3.06      0.75
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_motor_mdl, 'head_mean > 0')

## Hypothesis Tests for class b:
##        Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (head_mean) > 0     0.09      0.36     -0.5     0.68       1.53       0.6
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_motor_mdl, 'foot_leg_mean > 0')

## Hypothesis Tests for class b:
##            Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (foot_leg_mean) > 0     0.07      0.49    -0.73     0.89       1.24      0.55
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_motor_mdl, 'mouth_mean > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (mouth_mean) > 0     0.32      0.22    -0.04     0.69      12.49      0.93
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

hypothesis(other_all_motor_mdl, 'torso_mean > 0')

## Hypothesis Tests for class b:
##         Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob
## 1 (torso_mean) > 0     0.18       0.5    -0.63     1.02       1.81      0.64
##   Star
## 1     
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.

9.6 R-squared comparisons between models

First, let’s see how for all gestures, the iconicity model competes against the all sensory strength and all motor strength model:

bayes_R2(gesture_mdl)

##     Estimate  Est.Error      Q2.5    Q97.5
## R2 0.4875565 0.02610511 0.4349646 0.537166

bayes_R2(gesture_all_senses_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4915309 0.02622017 0.4374499 0.5409381

bayes_R2(gesture_all_motor_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4914347 0.02585352 0.4388202 0.5403105

Next, same thing for iconic gestures only:

bayes_R2(iconic_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4525314 0.03864714 0.3754943 0.5256872

bayes_R2(iconic_all_senses_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4665948 0.03773457 0.3899429 0.5385222

bayes_R2(iconic_all_motor_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4587925 0.03801456 0.3837259 0.5309054

Then for all other gestures:

bayes_R2(other_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4906281 0.02934794 0.4300478 0.5446238

bayes_R2(other_all_senses_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4951544 0.02871305 0.4369144 0.5490764

bayes_R2(other_all_motor_mdl)

##     Estimate  Est.Error      Q2.5     Q97.5
## R2 0.4973807 0.02874939 0.4390567 0.5502481

This completes this analysis.